Articlegreen2007

Generalized backward doubly stochastic differential equations and SPDEs with nonlinear Neumann boundary conditions

44 citations0/0 files storedBernoulli

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Stochastic processes and financial applications Nonlinear Partial Differential Equations Differential Equations and Boundary Problems

Abstract

In this paper a new class of generalized backward doubly stochastic differential equations is investigated. This class involves an integral with respect to an adapted continuous increasing process. A probabilistic representation for viscosity solutions of semi-linear stochastic partial differential equations with a Neumann boundary condition is given.

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References

1990Adapted solution of a backward stochastic differential equation 1990Stochastic Integration and Differential Equations 1984Stochastic differential equations with reflecting boundary conditions 1994Backward doubly stochastic differential equations and systems of quasilinear SPDEs 1998Generalized BSDEs and nonlinear Neumann boundary value problems 2001Stochastic viscosity solutions for nonlinear stochastic partial differential equations. Part I

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2008Stochastic PDIEs with nonlinear Neumann boundary conditions and generalized backward doubly stochastic differential equations driven by Lévy processes 2020Backward doubly stochastic Volterra integral equations and their applications

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