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

Brahim Boufoussi; Jan Van Casteren; N. Mrhardy

doi:10.3150/07-bej5092

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arXiv · 0708.4138

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

Brahim Boufoussi·Jan Van Casteren·N. Mrhardy

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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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Brahim Boufoussi, Jan Van Casteren, N. Mrhardy. 2007-08-30. Generalized backward doubly stochastic differential equations and SPDEs with nonlinear Neumann boundary conditions. https://doi.org/10.3150/07-bej5092

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