Stochastic viscosity solutions for SPDEs with continuous coefficients

In this note, nonlinear stochastic partial differential equations (SPDEs) with continuous coefficients are studied. Via the solutions of backward doubly stochastic differential equations (BDSDEs) with continuous coefficients, we provide an existence result of stochastic viscosity sub- and super-solu...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2011-12, Vol.384 (1), p.63-69
Main Authors: Djehiche, Boualem, Nʼzi, Modeste, Owo, Jean-Marc
Format: Article
Language:English
Subjects:
Applied mathematics
Backward doubly stochastic differential equation
MATEMATIK
MATHEMATICS
Stochastic partial differential equation
Stochastic viscosity solution
Tillämpad matematik
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Summary:In this note, nonlinear stochastic partial differential equations (SPDEs) with continuous coefficients are studied. Via the solutions of backward doubly stochastic differential equations (BDSDEs) with continuous coefficients, we provide an existence result of stochastic viscosity sub- and super-solutions to this class of SPDEs. Under some stronger conditions, we prove the existence of stochastic viscosity solutions.
ISSN:0022-247X
1096-0813
1096-0813
DOI:10.1016/j.jmaa.2010.08.005