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

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

2007-08-30

arxiv.org/abs/0708.4138v1

Bernoulli 2007, Vol. 13, No. 2, 423-446

Mathematics

Probability

Published at http://dx.doi.org/10.3150/07-BEJ5092 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statist

Scientific paper

10.3150/07-BEJ5092

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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