JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2017, Vol. 52 ›› Issue (4): 26-29.doi: 10.6040/j.issn.1671-9352.0.2016.327

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Comparison theorem for backward doubly stochastic differential equations driven by white noises and Poisson random measures

YANG Xu1, LI Shuo2*   

  1. 1. School of Mathematics and Information Science, Beifang University of Nationalities, Yinchuan 750021, Ningxia, China;
    2. Department of Mathematics, Changji University, Changji 831100, Xinjiang, China
  • Received:2016-07-06 Online:2017-04-20 Published:2017-04-11

Abstract: In this paper, a comparison theorem for a class of backward doubly stochastic differential equations driven by white noises and Poisson random measures was established.

Key words: white noises, Poisson random measure, backward doubly stochastic differential equations, comparison theorem

CLC Number: 

  • O211.6
[1] PARDOUX E, PENG S G. Backward doubly stochastic differential equations and systems of quasilimear SPDEs[J]. Probability Theory and Related Fields, 1994, 98(2):209-227.
[2] SHI Yufeng, GU Yanling, LIU Kai. Comparison theorem of backward doubly stochastic differential equations and applications[J]. Stochastic Analysis and Applications, 2005, 23(1):97-110.
[3] LIN Qian. Backward doubly stochastic differential equations with weak assumptions on the coefficients[J]. Applied Mathematics and Computation, 2011, 217(22):9322-9333.
[4] LIN Qian, WU Zheng. A comparison theorem and uniqueness theorem of backward doubly stochastic differential equations[J]. Acta Mathematicae Applicatae Sinica-English Series, 2011, 27(2):223-232.
[5] XIONG Jie. Super-brownian motion as the unique strong solution to an SPDE[J]. Annals of Probability, 2013, 41(2):1030-1054.
[6] HE Hui, LI Zenghu, YANG Xu. Stochastic equations of super-Lévy processes with general branching mechanism[J]. Stochastic Processes and Applications, 2014, 124(4):1519-1565.
[7] 杨叙, 李硕. 一类带跳倒向重随机微分方程解的轨道唯一性[J]. 通化师范学院学报, 2015,36(5):31-33. YANG Xu, LI Shuo. Pathwise uniqueness for a class backward doubly SDEs with jumps[J].Journal of Tonghua Normal University, 2015, 36(5):31-33.
[8] XU Wei. Backward doubly stochastic equations with jumps and comparison theorems[J]. Journal of Mathematical Analysis and Applications, 2016, 443(1):596-624.
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