Results 261 to 270 of about 208,713 (299)

Stochastic Partial Differential Equations

2007
Preliminaries Introduction Some Examples Brownian Motions and Martingales Stochastic Integrals Stochastic Differential Equations of Ito Type Levy Processes and Stochastic Integrals Stochastic Differential Equations of Levy Type Comments Scalar Equations of First Order Introduction Generalized Ito's Formula Linear Stochastic Equations Quasilinear ...
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Stochastic Partial Differential Equations

2012
A brief discussion on the relevance of stochastic partial differential equations (SPDEs) in Sect. 9.1 is followed by a review of the type of SPDEs studied in the mathematical literature (Sect. 9.2). Section 9.3 shows that SPDEs can be solved by the methods in Chaps. 7 and 8 via time and space discretization.
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Stochastic Partial Differential Equations

2016
So far, we have discussed discrete interface models. Taking their (mesoscopic) continuum limit, as a time evolution of interfaces or some other related physical order parameters, one would expect to obtain stochastic partial differential equations (SPDEs), which are partial differential equations having stochastic terms such as a space-time Gaussian ...
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Tsirel'son's Example for Stochastic Partial Differential Equations

Acta Mathematica Hungarica, 2001
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On the approximation of stochastic partial differential equations i

Stochastics, 1988
The stability of abstract stochastic partial differential equations with respect to the simultaneous perturbation of the driving processes and of the differential operators is investigated. The results obtained here will be applied to concrete stochastic partial differential equations in the continuation of this ...
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Difference Methods for Stochastic Partial Differential Equations

ZAMM, 2002
The deterministic theory of finite difference schemes is an important subject in order to approximate the solutions of partial differential equations. This article presents difference methods in order to approximate the solutions of stochastic partial differential equations of Itô-type, in particular hyperbolic equations.
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Stochastic Equations and Stochastic Methods in Partial Differential Equations

2006
In the first part of the paper, basic notions of stochastic analysis and probability theory are recalled, including the concept of stochastic integration, and some basic results of the theory of partial differential equations are reviewed. The second part of the paper is a review of applications of stochastic analysis techniques in deterministic PDE ...
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A stochastic partial differential equation for computational algorithms

Applied Mathematics and Computation, 2004
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Stochastic partial differential equations on manifolds,I

Potential Analysis, 1993
The author considers the problem \[ du(f,x)=({\mathcal L}u(t,x) + f(t,x))dt+ ({\mathcal N}^ l(t,x)u(t,x)+ g^ l(t,x))dW^ l(t), \quad u(0,x)=u_ 0(x), \] \(x\in M\), where \((W^{\l},{\mathcal F}_ t)\) is a \(d_ 1\)- dimensional Wiener process on a stochastic basis \((\Omega,{\mathcal F},P,({\mathcal F}_ t))\), \({\mathcal L}\) is a second order and ...
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On a Class of Stochastic Partial Differential Equations

Theory of Probability & Its Applications, 1983
Belopol'skaya, Ya. I., Nagolkina, Z. I.
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