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Stochastic Viscosity Solutions for SPDEs with Discontinuous Coefficients
College of Science, North China University of Technology, Beijing, China
- 1 College of Science, North China University of Technology, Beijing, China
Applied Mathematics·Volume 11 (2020)·Pages 1219–1228·Published 2 November 2020·DOI10.4236/am.2020.1111083
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Abstract
In this paper, a class of nonlinear stochastic partial differential equations with discontinuous coefficients is investigated. This study is motivated by some research on stochastic viscosity solutions under non-Lipschitz conditions recently. By studying the solutions of backward doubly stochastic differential equations with discontinuous coefficients and constructing a new approximation function f n to the coefficient f , we get the existence of stochastic viscosity sub-solutions (or super-solutions).The results of this paper can be seen as the extension and application of related articles.
KeywordsStochastic Partial Differential EquationStochastic Viscosity SolutionBackward Doubly Stochastic Differential Equation
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