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| Backward Doubly Stochastic Differential Equations with Jumps and Stochastic Partial Differential-Integral Equations |
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Citation： |
Qingfeng ZHU,Yufeng SHI.Backward Doubly Stochastic Differential Equations with Jumps and Stochastic Partial Differential-Integral Equations[J].Chinese Annals of Mathematics B,2012,33(1):127~142 |
| Page view： 2889
Net amount： 2655 |
Authors： |
Qingfeng ZHU; Yufeng SHI; |
Foundation： |
the National Natural Science Foundation of China (Nos. 10771122, 11071145), the Shandong Provincial Natural Science Foundation of China (No. Y2006A08), the Foundation for Innovative Research Groups of National Natural Science Foundation of China (No. 10921101), the National Basic Research Program of China (the 973 Program) (No. 2007CB814900) and the Independent Innovation Foundation of Shandong University (No. 2010JQ010). |
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| Abstract： |
Backward doubly stochastic differential equations driven by Brownian motionsand Poisson process (BDSDEP) with non-Lipschitz coefficients on random time intervalare studied. The probabilistic interpretation for the solutions to a class of quasilinearstochastic partial differential-integral equations (SPDIEs) is treated with BDSDEP. Undernon-Lipschitz conditions, the existence and uniqueness results for measurable solutionsto BDSDEP are established via the smoothing technique. Then, the continuous dependencefor solutions to BDSDEP is derived. Finally, the probabilistic interpretation for thesolutions to a class of quasilinear SPDIEs is given. |
Keywords： |
Backward doubly stochastic differential equations, Stochastic partial differential-integral equations, Random measure, Poisson process |
Classification： |
60H10,60G55,60H15 |
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