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Tsirel'son's Example for Stochastic Partial Differential Equations
Acta Mathematica Hungarica, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Difference Methods for Stochastic Partial Differential Equations
ZAMM, 2002The 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 Partial Differential Equations
1995Stochastic partial differential equations can be used in many areas of science to model complex systems that evolve over time. Their analysis is currently an area of much research interest. This book consists of papers given at the ICMS Edinburgh meeting held in 1994 on this topic, and it brings together some of the world's best known authorities on ...
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On the approximation of stochastic partial differential equations i
Stochastics, 1988The 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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Stochastic Equations and Stochastic Methods in Partial Differential Equations
2006In 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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On a Class of Stochastic Partial Differential Equations
Theory of Probability & Its Applications, 1983Belopol'skaya, Ya. I., Nagolkina, Z. I.
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Stochastic partial differential equations on manifolds,I
Potential Analysis, 1993The 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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Solving a Nonlinear Fractional Stochastic Partial Differential Equation with Fractional Noise
, 2016Junfeng Liu, Litan Yan
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