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

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.

Published at http://dx.doi.org/10.3150/07-BEJ5092 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

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• Stochastic viscosity solutions for stochastic integral-partial differential equations and singular stochastic control