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Multivalued Stochastic Partial Differential-Integral Equations Via Backward Doubly Stochastic Differential Equations Driven by a Lévy Process

Volume 13, Number 2 (2012), 1 - 22

Multivalued Stochastic Partial Differential-Integral Equations Via Backward Doubly Stochastic Differential Equations Driven by a Lévy Process

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Abstract

In this paper, we deal with a class of backward doubly stochastic differential equations (BDSDEs, in short) involving subdifferential operator of a convex function and driven by Teugels martingales associated with a L\'{e}vy process. We show the existence and uniqueness result by means of Yosida approximation. As an application, we give the existence of stochastic viscosity solution for a class of multivalued stochastic partial differential-integral equations (MSPIDEs, in short).