Stochastic viscosity solutions for SPDEs with continuous coefficients |
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| Authors: | Boualem Djehiche |
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| Institution: | a Department of Mathematics, The Royal Institute of Technology (KTH), SE-100 44 Stockholm, Sweden
b Université de Cocody, UFR de Mathématiques et Informatique, 22 BP 582 Abidjan, Cote d?Ivoire |
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| Abstract: | 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. |
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| Keywords: | Stochastic partial differential equation Backward doubly stochastic differential equation Stochastic viscosity solution |
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