... Abstract : First an investigation of modeling stochastic processes by difference equations (Markov process) was undertaken. ...
DTIC Science & Technology
... Abstract : The Lagrange expansion, which may be used to derive the Fokker-Planck equation, is here to derive the corresponding expression for ...
This paper is essentially an application of the author's theory of abstract stochastic bilinear equations to the problem of laser beam propagation in a turbulent medium, and the associated random Schroedinger equation. The white noise theory is shown to p...
National Technical Information Service (NTIS)
... ESTIMATES, *STATISTICAL SAMPLES, MEAN, LINEAR ALGEBRAIC EQUATIONS, QUADRATIC EQUATIONS, INTEGRALS, STOCHASTIC ...
... PROGRAMMING, *STOCHASTIC CONTROL, TRANSFORMATIONS( MATHEMATICS), QUADRATIC EQUATIONS, DIFFERENTIAL EQUATIONS ...
... STOCHASTIC PROCESSES, *GAUSSIAN NOISE, *NONLINEAR ANALYSIS, DIFFERENTIAL EQUATIONS, INTEGRAL EQUATIONS, CALCULUS. ...
... of the Stochastic Advection Equation ... 4. TITLE AND SUBTITLE Spectral Polynomial Chaos Solutions of the Stochastic Advection Equation 5a. ...
Jan 22, 2011 ... Abstract: A nonlinear version of the Liouville equation based upon terminal attractors is proposed for describing post-instability motions ...
NASA Website
... Abstract : The dynamical behavior of laser-stimulated surface processes (LSSP) is studied by the generalized Langevin equation via the memory ...
The long-time behaviour of a stochastic 3D LANS-{alpha} model on a bounded domain is analysed. First, we reformulate the model as an abstract problem. Next, we establish sufficient conditions ensuring the existence of stationary (steady state) solutions of this abstract nonlinear stochastic evolution ...
Energy Citations Database
Existence and uniqueness theorems for stochastic evolution equations are developed in a Hilbert space context. The results are based on a blending of the theorems for evolution equations with stochastic integration for Hilbert space valued random processe...
Dynamics for the stochastic Kuramoto-Sivashinsky equation with a nonlocal term is studied. We prove that the stochastic equation has a finite-dimensional random attractor.
NASA Astrophysics Data System (ADS)
... STATISTICAL INFERENCE, SIGNALS, SAMPLING, PARTIAL DIFFERENTIAL EQUATIONS, DIFFERENTIAL EQUATIONS, EQUATIONS ...
... Title : Research on Deterministic and Stochastic Partial Differential Equations with Applications to Continuum Physics and Stochastic Systems ...
... loop control of stochastic systems is treated. The system is assumed to be modeled by a stochastic differential equation and the admissible controls ...
Some aspects of stochastic quantization and stochastic partial differential equations are investigated using systematically stochastic calculus. The stochastic quantization is considered as a special case of the theory of the stochastic partial differenti...
Aspects of the theory of continuous stochastic processes that seem to contribute to an understanding
NASA Technical Reports Server (NTRS)
... Descriptors : *WAVE EQUATIONS, MATHEMATICAL MODELS, OPTIMIZATION, STOCHASTIC PROCESSES, TWO DIMENSIONAL, MATRICES ...
... ANALYSIS, *GAME THEORY, OPTIMIZATION, STOCHASTIC PROCESSES, COEFFICIENTS, QUADRATIC EQUATIONS, CONTROL THEORY. ...
... Accession Number : ADA095241. Title : Singular Perturbations, Stochastic Differential Equations, and Applications,. Corporate ...
Stability of stochastic processes defined by difference differential equations, noting properties of
... The main class of problems was concerned with regularity properties of solutions to stochastic wave equations in one and two spatial dimensions. ...
... Title : Asymptotic Analysis of Stochastic Differential Equations and Their Applications in Diffusion Theory, Stability of Structures and Reliability ...
Galactic stochastic magnetic field lines, deriving dynamic equation for probability density function
We deal with abstract systems of two coupled nonlinear stochastic (infinite dimensional) equations subjected to additive white noise type process. This kind of systems may describe various interaction phenomena in a continuum random medium. Under suitable conditions we prove the existence of an exponentially attracting random invariant ...
together with the resulting stochastic dynamic programming equation are presented. .... ell man's equation or stochastic dynamic programming ...
This paper sets out to show how to deal with stochastic differential equations on manifolds in which the equation is governed by a Poisson stochastic measure. In section 2, we show how to integrate with respect to Poisson stochastic measures and in sectio...
... Title : Stochastic Duels with Displacements (Suppression ... Abstract : The stochastic duel is extended to include the possibility of a near-miss on each ...
... Title : Stochastic Calculus and Survival Analysis. ... Abstract : This paper gives a brief survey of the uses of stochastic calculus in survival analysis. ...
... Accession Number : ADA545706. Title : Some Topics in Stochastic Control. ... Abstract : Several Topics in Stochastic Analysis are studied. ...
The cubically nonlinear Schroedinger equation is an important model of nonlinear phenomena in fluids
... PROCESSES, OPTIMIZATION, PROBABILITY DENSITY FUNCTIONS, DIFFERENCE EQUATIONS, DIFFERENTIAL EQUATIONS, CONTROL ...
A continuous model for a nondemolition observation of an atom is given. An equation for the corresponding instrument is found and a stochastic dissipative Schroedinger equation for the unnormalized posterior wave function of the atom is derived. The conti...
... In these limits the dynamics of the mass defect particle is exactly described by a Fokker-Planck equation, ie a stochastic equation of motion. ...
Stochastic equations with small random terms are considered. A perturbation method is applied to obtain an equation satisfied by the expected solution of such a stochastic equation. The method is then applied to wave propagation in random continuous media...
Semilinear parabolic differential equations are solved in a mild sense in an infinite-dimensional Hilbert space. Applications to stochastic optimal control problems are studied by solving the associated Hamilton-Jacobi-Bellman equation. These results are applied to some controlled stochastic partial differential ...
Just as introduction of stochastic parameters into Newton equation (transition to Langevin equation) allows one to describe open quantum system, the Schroedinger equation with stochastic classical noise is a good model for description of open quantum syst...
This paper is essentially an application of the author's theory of abstract stochastic bilinear equations to the problem of laser-beam propagation in a turbulent medium, and the associated random Schroedinger equation. The white noise theory is shown to provide a consistent self-contained model for the ...
Abstract. We present approaches for the study of fluid-structure interactions subject to thermal fluctuations. A mixed mechanical description is utilized combining Eulerian and Lagrangian reference frames. We establish general conditions for operators coupling these descriptions. Stochastic driving fields for the formalism are derived using principles from ...
E-print Network
Abstract. We present numerical schemes for the strong solution of linear stochastic differential equations driven by an arbitrary number of Wiener processes. These schemes are based on the Neumann (stochastic Taylor) and Magnus expansions. Firstly, we consider the case when the governing linear diffusion vector ...
We develop a stochastic generalization of the McLachlan variational principle and show that it can be used to derive known stochastic wave equations. We then use it to obtain an exact probability preserving stochastic density decomposition for vibrational dynamics problems with pairwise interaction. PMID:12636634
PubMed
Outgoing from a time-dependent theory of correlations, we present a stochastic differential equation for the propagation of ensembles of Slater determinants, called Stochastic Time-Dependent Hartree-Fock (Stochastic TDHF). These ensembles are allowed to d...
We establish the existence and uniqueness of both local martingale and local pathwise solutions of an abstract nonlinear stochastic evolution system. The primary application of this abstract framework is to infer the local existence of strong, pathwise solutions to the 3D primitive equations of the oceans and ...
... will be either the Euler equations or the quasi- linear unsteady potential ... of entropy solutions for stochastic hyperbolic systems of conservation laws ...
... Accession Number : ADA460601. Title : Spectral Polynomial Chaos Solutions of the Stochastic Advection Equation. Corporate ...
The approximation, which is of the spectral stochastic finite element type, .... originating in the discretization of partial differential equations) and m is relatively ...
... Title : Reproducing Kernel Spaces and Stochastic Multivariate Differential Equations with a Deterministic Control Theory Application. ...
... Title : Random Fields Governed by Stochastic Partial Differential Equations and Their Applications to Oceanography. Descriptive Note : Final rept. ...
Introducing the generalized Langevin equation, we extend the stochastic quantization method so as to
... The main task was to state an appropriate stochastic Fermat's principle whose implementation would render stochastic type Eikonal equations for ...
In this paper a new approach to the control of systems represented by stochastic differential equations (SDEs) is developed in which stochastic control is viewed as deterministic control with a particular form of constraint structure. Specifically, the ch...
The mathematical foundation of the Ito interpretation of stochastic ordinary and partial differential equations is briefly explained. This provides the basis for a review of simple difference approximations to stochastic differential equations. An example arising in the theory of optical switching is discussed.
DOE Information Bridge
Semilinear elliptic partial differential equations are solved in a mild sense in an infinite-dimensional Hilbert space. These results are applied to a stochastic optimal control problem with infinite horizon. Applications to controlled stochastic heat and wave equations are given.
The stochastic quantization in lattice gauge theories (LGT) is discussed by using Langevin equations and Fokker-Planck equations. It is shown that the evolution equations in the stochastic process reduce to the Schwinger-Dyson equation when the lattice system reaches ...
... Title : Workshop/School on Stochastic Partial Differential Equations: Theory and Applications. Descriptive Note : Final technical rept. ...
Radiative transfer equations are derived for a medium with small stochastically defined opacity and energy fluctuations. These equations provide relations between the correlation functions connecting these fluctuations and the induced fluctuations in the ...
... Title : Stochastic Differential Equations in Duals of Nuclear Spaces with Some Applications. Descriptive Note : Technical rept. 30 Sep 85-30 Sep 86,. ...
... that of solving a stochastic Dynamic Programming equation [Al, BI ... 6 Page 16. the stochastic dynamic programming equation (see also Meier [Ml]): ...
The two-time method is used to obtain an expansion, valid for epsilon small and t large, of the vector solution u(t,epsilon) of an abstract ordinary differential equation involving epsilon. The same method is used to get expansions of functions of u. The ...
A Wick-type stochastic Korteweg-de Vries equation is researched. We establish a relationship between the Korteweg-de Vries equation and the elliptic equation. With the help of Hermit transformation and the elliptic equation mapping method, we obtain a series of exact Jacobi elliptic function ...
CONTENTSIntroduction � 1. The finite-dimensional case � 2. Stochastic semigroups in the L2-strong theory � 3. Homogeneous strongly continuous semigroups with the group of the first moments � 4. Stochastic equations of diffusion type with constant coefficients � 5. Continuous homogeneous stochastic ...
The stochastic field approach describes grain growth in polycrystalline materials as a stochastic process in volume time space. A stochastic process represented by a Fokker-Planck equation in volume time space automatically conserves the volume of the specimen. The stochastic component of grain ...
... Title : Random Walks and Generalized Master Equations with Internal Degrees of Freedom (Stochastic Processes/Transport Phenomena),. ...
... The Fokker-Planck equation approach is used to derive a general differential equation for the response joint moments. ...
... for the solution of the partial differential equation for the joint probability density function of the state variable, ie, the Fokker-Planck Equation. ...
... which should properly be described by linear differential equations ... solution of either ordinary or partial linear differential equations ...
In this thesis, several approaches to stochastic dynamics in storage rings are investigated. In the first part the theory of stochastic differential equations and Fokker-Planck equations is used to describe the processes which have been assumed to be Mark...
Stochastic quantization in Minkowski space is discussed in detail. The Fokker-Planck equation corresponding to the complex Langevin equation is derived and solved explicitly in the case of free scalar fields. It turns out that Minkowski stochastic quantization can be formulated in terms of a real positive ...
In this paper we prove the existence of a solution to backward stochastic differential equations in infinite dimensions with continuous driver under various assumptions. We apply our results to a stochastic game problem with infinitely many players.
The problem of stochastization of the initial conditions is studied numerically within the framework of the nonlinear Klein--Gordon equation. A specific case of the classical Yang--Mills equations is shown to identify the absence of stochastization.
The purpose of this paper is to establish the theory of stochastic pseudo-differential operators and give its applications in stochastic partial differential equations. First, we introduce some concepts on stochastic pseudo-differential operators and prove their fundamental properties. Also, we present the ...
... stochastic process that satisfies the simple condition that ... Walker equations, which are derived, determine the autocovariance sequence. ...
... Title : THE CAUCHY PROBLEM FOR DEGENERATE PARABOLIC EQUATIONS OF STOCHASTIC CONTROL THEORY,. ...
A nonlinear version of the Liouville equation based on terminal attractors is part of a mathematical
Stochastic versions of stability equations are considered as a means to develop integrated models of
... COMMUNICATIONS, CONTROL THEORY, APPLIED MATHEMATICS, NONLINEAR ALGEBRAIC EQUATIONS, VARIATIONAL METHODS. ...
... procedure. First, the logistic equation of population dynamics is studied in deterministic and stochastic versions. Second ...
... Descriptors : (*EQUATIONS, STOCHASTIC PROCESSES), (*NEUTRON TRANSPORT THEORY, INVARIANCE), STATISTICAL PROCESSES ...
... the finite difference solutions to the ... the weak sense solution to the ... DIFFERENTIAL EQUATIONS, STOCHASTIC PROCESSES, MEASURE ...
... SYSTEMS, OPTIMIZATION), (*STOCHASTIC PROCESSES, THEORY), EQUATIONS, LEAST SQUARES METHOD, MATRICES(MATHEMATICS ...
Circadian modulation of episodic bursts is recognized as the normal physiological pattern of diurnal
... Descriptors : *CURVE FITTING, *OSMIUM COMPOUNDS, COMPLEX VARIABLES, DISTRIBUTION THEORY, EQUATIONS, FUNCTIONS ...
We consider a stochastic Burgers type equation which incorporates a vector potential. The solution of this equation is not of gradient form and so this equation can be described as a stochastic Burgers equation with vorticity. Building on previous work on the standard ...
... Title : Stochastic Control of Queueing Systems. ... Abstract : Suppose that the state of a queueing system is described by a Markov process ((Y sub t), t ...
... Abstract : This paper is a sequel to AD-637 139 in which stochastic programs with recourse were formulated as a generalization of the two-stage ...
... Title : A Stochastic Model of a Repairable Item Inventory System. ... Abstract : An inventory system for repairable items is studied. ...
An improved algorithm is devised for using Fan sub-equation method to solve Wick-type stochastic partial differential equations. Applying the improved algorithm to the Wick-type generalized stochastic KdV equation, we obtain more general Jacobi and Weierstrass elliptic function solutions, ...
Linear stochastic master equations for wave propagation in an continuous random medium are derived along the lines of the resolvent theory used in nonequilibrium statistical mechanics. Equations for the mean and fluctuating fields are subsequently obtaine...
The solution of a generalized Langevin equation is referred to as a stochastic process. If the external forcing function is Gaussian white noise, the forward Kolmogarov equation yields the transition probability density function. Nonlinear problems must b...
This paper derives stochastic differential equations for recursive maximum likelihood estimates for the joint filtering parameter estimation problem. Keywords: Maximum likelihood estimates; Stochastic differential equation; Hamilton Jacobi equation; Nonli...
We study the Langevin equation for stochastic quantization of gravity. By introducing two independent variables with a second-class constraint for the gravitational field, we formulate a pair of the Langevin equations for gravity which couples with white ...
The coupled Kadomtsev-Petviashvili (KP) equations with variable coefficients and Wick-type stochastic coupled KP equations are investigated. Exact solutions are shown using the Hermite transform, the homogeneous balance principle and the F-expansion method.
An important step in the modeling of dynamic systems is in the validation of the model equations with experimental data or observations. If the model is described by either nonlinear or partial differential equations, analytical or closed form solutions a...
In this paper we discuss the controllability of a wave equation with random noise. Our main tools are the Ito representation theorem and an adaptation of the Hilbert uniqueness method for the exact controllability of deterministic equations.
In this paper, the stochastic asymptotical stability of stochastic impulsive differential equations is studied, and a comparison theory about the stochastic asymptotical stability of trivial solution is established. From the comparison theory, we can find out whether the stochastic impulsive ...
... Abstract : A set of coupled integral equations is derived from the incompressible Navier-Stokes equations and the continuity equation. ...
This study considers q-Gaussian distributions and stochastic differential equations with both multiplicative and additive noises. In the M-dimensional case a q-Gaussian distribution can be theoretically derived as a stationary probability distribution of the multiplicative stochastic differential equation with both ...
In this paper, the generally projective Riccati equations method is improved by means of a generalized transformation. The improved method can be applied to find not only some exact travelling wave solutions but also some soliton-like solutions with the aid of symbolic computation system � Maple. We choose Wick-type stochastic mKdV ...
The focus of this work is on a two-dimensional stochastic vorticity equation for an incompressible homogeneous viscous fluid. We consider a signed measure-valued stochastic partial differential equation for a vorticity process based on the Skorohod-Ito evolution of a system of N randomly moving point vortices. A ...
The aim of the paper is to obtain new characterizations for exponential stability in mean square of stochastic variational systems in Hilbert spaces. Thus we will introduce a general concept of admissibility in variational stochastic case. An example of such a stochastic variational system is considered the parabolic ...
An attempt to describe the dose dependence of cell inactivation by a stochastic differential equation is made. For this, a stochastic variable in dose radiosensitivity is introduced. Some solutions of the stochastic equation are obtained and and analyzed. How to obtain the value of the noise ...
Within the framework of the Kershaw approach and of a hypothesis on spatial stochasticity, the relativistic equations of Lehr and Park, Guerra and Ruggiero, and Vigier for stochastic Nelson mechanics are obtained. In our model there is another set of equations of the hydrodynamical type for the drift velocity v i( ...
Abstract�Consider the problem of developing a controller for general (nonlinear and stochastic) systems where the equations governing the system are unknown. Using discrete-time measurements, this paper presents an approach for estimating a controller without building or assuming a model for the system (including such general models ...
The Fokker-Planck and backward Kolmogorov equations are formulated for a dynamic system with a small stochastic perturbation. The dynamics of the deterministic hypercycle are described. The asymptotic approximation of the expected exit time for the attrac...
... Accession Number : ADA015916. Title : Stochastic Control of Systems Governed by Partial Differential Equations. Descriptive Note : Interim rept.,. ...
A relativistic extension of stochastic mechanics is proposed. The starting point is the construction of relativistically covariant diffusions satisfying a property similar but not identical to the Markov property. It is shown that the continuity equation ...
It is only required that z(t ) be square integrable over the interval of integration ..... Stochastic Differential Equations II, International Journal of ...
Page 1. Diagnosability of Stochastic Chemical Kinetic Systems: A Discrete Event ... 10. The proof of correctness for the discrete-update equation Eq. ...
An averaged system to approximate the slow dynamics of a two timescale nonlinear stochastic control system is introduced. Validity of the approximation is established. Special cases are considered to illustrate the general theory.
A stochastic model of grain surface chemistry, based on a master equation description of the probability distributions of reactive species on grains, ...
We consider a general class of problems of the minimization of convex integral functionals subject to linear constraints. Using Fenchel duality, we prove the equality of the values of the minimization problem and its associated dual problem. This equality is a variational criterion for the existence of a solution to a large class of inverse problems entering the class of generalized Fredholm ...
Abstract. A model with wealth accumulation subject to i.i.d. random shocks is examined. The transfer function shows what kt+1- wealth at t + 1- would be, given kt, with no shock. It has a positive slope, but indeterminate concavity/convexity. The stationary distribution satis�es a Fredholm integral equation and can be examined by direct analysis of the ...
Time evolution of a quantum system which is influenced by a stochastically fluctuating environment is studied by means of the stochastic Liouville equation. The two different types of the stochastic Liouville equation and their relation are discussed. The stochastic ...
Abstract: Convergence rates of adaptive algorithms for weak approximations of It� stochastic differential equations are proved for the Monte Carlo Euler method. Two algorithms based either on optimal stochastic time steps or optimal deterministic time steps are studied. The analysis of their computational ...
Abstract. In this paper we deal with the numerical approximation of integro-differential equations arising in financial applications in which jump processes act as the underlying stochastic processes. Our aim is to find finite differences schemes which are high-order accurate for large time regimes. Therefore, we study the asymptotic ...
An important and well established area of quantum optics is the theory of Markovian stochastic Schr�dinger equations (or by another name quantum trajectory theory). Recently stochastic Schr�dinger equations have been developed for non-Markovian systems. In this paper we extend the current known ...
The stochastic equations of evolution of lateral energy of the fast charged channeled particles is obtained from the condition of nonpreservation of the adiabatic invariant. The electric potential of the crystal is presented in form of the sum of its average value and the potential fluctuation, caused by the thermal oscillations of the atomic nuclei and ...
Invariant manifolds play an important role in the study of the qualitative dynamical behaviors for nonlinear stochastic partial differential equations. However, the geometric shape of these manifolds is largely unclear. The purpose of the present paper is to try to describe the geometric shape of invariant manifolds for a class of ...
Time-independent wave propagation is treated in media where the index of refraction contains a random component, but its mean is invariant with respect to translation in some direction distinguishing the wave propagation. Abstract splitting operators are used to decompose the wave field into forward and backward traveling components satisfying a coupled pair of ...
dimensional version of the Malliavin calculus to show positivity and regularity of the invariant measureUniqueness of the Invariant Measure for a Stochastic PDE Driven by Degenerate Noise September 15�Landau equation. Under these assumptions, we show that the stochastic PDE has a unique invariant measure
STOCHASTIC DIFFERENTIAL SYSTEMS WITH MEMORY Salah-Eldin A. Mohammed Research monograph. Preliminary-0203368 and DMS-0705970. 1 #12;Preface The impetus for writing this research monograph is two-fold: During of the author's monograph Stochastic Functional Differential Equations (sfde's) in 1984, there have been
In models with stochastic modification of the Schroedinger equation, the Schroedinger expansion of the wave function is interrupted by repeated spontaneous stochastic localizations, called 'quantum jumps'. In the K-model, this stochastic modification of t...
The problem of optimal open-loop control of stochastic systems is treated. The system is assumed to be modeled by a stochastic differential equation and the admissible controls are taken to be deterministic functions of time. The optimal control is the co...
discussed in the literature of stochastic field theories. A mean�field formulation of the dynamical problem of the color fields of non�Abelian gauge theories in the high temperature regime, as a stochastic classical the associated Langevin mean�field equation, but with the stochastic averages already taken ...
This paper is concerned with the study of the properties of the Stochastic EM estimator. The Stochastic EM estimator is an estimator derived from an iterative algorithm which handles statistical model with missing data. The first result we obtain is on the decomposition of a general stochastic difference equation ...
A notion of stochastic deformation is introduced and the corresponding algebraic deformation procedure is developed. This procedure is analogous to the deformation of an algebra of observables like deformation quantization, but for an imaginary deformation parameter (the Planck constant). This method is demonstrated on diverse relativistic and nonrelativistic models with ...
... Title : NOMOGRAM FOR SAHA'S EQUATION. ... Abstract : In the report a nomogram for the solution of Saha's equation is given. ...
... Title : BROADENING IN THE MASTER EQUATION. ... Abstract : Broadening has been introduced into the collision term of the master equation. ...
This paper is concerned with the stochastic linear quadratic optimal control problem (LQ problem, for short) for which the coefficients are allowed to be random and the cost functional is allowed to have a negative weight on the square of the control variable. Some intrinsic relations among the LQ problem, the stochastic maximum principle, and the (linear) ...
a deterministic, homogenized (effective medium) equation or a stochastic equation with multiplicative noise. More for systems with many invariant measures Long-time effect caused by deterministic and stochastic perturba: Convergence to deterministic or stochastic limits and theory of correctors ...
We present nonlinear stochastic differential equation (SDE) which forms the background for the stochastic modeling of return in the financial markets. SDE is obtained by the analogy with earlier proposed model of trading activity in the financial markets and generalized within the nonextensive statistical mechanics framework. Proposed ...
The Brownian motion on a Riemannian manifold is a stochastic process such that the heat kernel is the density of the transition probability. If the total probability of the particle being found in the state space is constantly 1, then the Brownian motion is called stochastically complete. For manifolds with time-dependent metrics, the heat ...
A stochastic optimal control strategy for a slightly sagged cable using support motion in the cable axial direction is proposed. The nonlinear equation of cable motion in plane is derived and reduced to the equations for the first two modes of cable vibration by using the Galerkin method. The partially averaged It� ...
A Hamiltonian formalism is developed for the drift orbit trajectories of particles in toroidal systems in the presence of stochastic fields. The equations of motion are integrated numerically to investigate the modification of neoclassical diffusion in a Tokamak due to the onset of stochasticity. Quasilinear diffusion is observed for ...
