JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2015, Vol. 50 ›› Issue (08): 24-33.doi: 10.6040/j.issn.1671-9352.0.2015.038

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Multidimensional backward doubly stochastic differential equations with generators of Osgood type

WANG Xian-fei, JIANG Long, MA Jiao-jiao   

  1. College of Sciences, China University of Mining and Technology, Xuzhou 221116, Jiangsu, China
  • Received:2015-01-09 Online:2015-08-20 Published:2015-07-31

Abstract: A class of multidimensional backward doubly stochastic differential equations whose generator f satisfies the Osgood condition in y and generator g satisfies non-Lipschitz condition in y was studied. An existence and uniqueness theorem and a stability theorem of solutions for this kind of equations were established, and a comparison theorem for solution of the class of one-dimensional situation was proposed.

Key words: backward doubly stochastic differential equations, Osgood condition, existence and uniqueness theorem, stability theorem, comparison theorem

CLC Number: 

  • O211
[1] NUALART D, PARDOUX E. Stochastic calculus with anticipating integrands[J]. Probability Theory Related Fields, 1988, 78(4): 535-581.
[2] FAN Shengjun, JIANG Long, DAVISON M. Uniqueness of solutions for multidimensional BSDEs with uniformly continuous generators[J]. Comptes Rendus Mathematique, 2010, 348: 683-686.
[3] FAN Shengjun, JIANG Long. Multidimensional BSDEs with weak Monotonicity and general growth generators[J]. Acta Mathematica Sinica, English Series, 2013, 23(10): 1885-1906.
[4] FAN Shengjun, JIANG Long, DAVISON M. Existence and uniqueness result for multidimensional BSDEs with generators of Osgood type[J]. Frontiers of Mathematics in China, 2013, 8(4): 811-824.
[5] LIN Qian. A class of backward doubly stochastic differential equations with non-Lipschitz coefficients[J]. Statistic and Probability Letters, 2009, 79(20): 2223-2229.
[6] LIN Qian. A generalized existence theorem of backward doubly stochastic differential equations[J]. Acta Mathematica Sinica, English Series, 2010, 26(8): 1525-1534.
[7] PARDOUX E, PENG Shige. Adapted solution of a backward stochastic differential equation[J]. Systems Control Letters, 1990, 14(1): 55-61.
[8] PARDOUX E, PENG Shige. Backward doubly stochastic differential equation and systems of quasilinear parabolic SPDEs[J]. Probability Theory Related Fields, 1994, 98(2): 209-227.
[9] SHI Yufeng, GU Yanling, LIU Kai. Comparison theorem of backward doubly stochastic differential equations and applications[J]. Stochastic Analysis and Application, 2005, 23(1): 97-110.
[10] 周少甫, 曹小勇, 郭潇. 倒向双重随机微分方程[J]. 应用数学, 2004, 17(1): 95-103. ZHOU Shaofu, CAO Xiaoyong, GUO Xiao. Backward doubly stochastic differential equations[J]. Mathematica Applicata, 2004, 17(1):95-103.
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