Backward Doubly Stochastic Differential Equations with Jumps and Stochastic Partial Differential-Integral Equations

Details Backward Doubly Stochastic Differential Equations with Jumps and Stochastic Partial Differential-Integral Equations Backward Doubly Stochastic Differential Equations with Jumps and Stochastic Partial Differential-Integral Equations

2010-05-14

arxiv.org/abs/1005.2474v1

Mathematics

Probability

19 pages

Scientific paper

In this paper, we study backward doubly stochastic differential equations driven by Brownian motions and Poisson process (BDSDEP in short) with non-Lipschitz coefficients on random time interval. The probabilistic interpretation for the solutions to a class of quasilinear stochastic partial differential-integral equations (SPDIEs in short) is tthe solutionBDSDEP. Under non-Lipschitz conditions, the existence and uniqueness results for measurable solutions of BDSDEP are established via the smoothing technique. Then, the continuous dependence for solutions of BDSDEP is derived. Finally, the probabilistic interpretation for the solutions to a class of quasilinear SPDIEs is given.

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