华东师范大学学报(自然科学版) ›› 2010, Vol. 2010 ›› Issue (3): 119-125.

• 应用数学与基础数学 • 上一篇    下一篇

系数为广义左Lipschitz的倒向随机微分方程解的存在性

田德建, 江龙,邓芳   

  1. 中国矿业大学理学院, 徐州 221116
  • 收稿日期:2009-10-30 修回日期:2010-01-13 出版日期:2010-05-25 发布日期:2010-05-25
  • 通讯作者: 田德建

On existence of solutions to backward stochastic differential equation with generalized left-Lipschitz coefficients

TIAN De-jian, JIANG Long, DENG Fang   

  1. School of Sciences, China University of Mining and Technology, Xuzhou221116, China
  • Received:2009-10-30 Revised:2010-01-13 Online:2010-05-25 Published:2010-05-25
  • Contact: TIAN De-jian

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摘要： 证明了一类生成元满足广义左Lipschitz条件的倒向随机微分方程解的存在性.通过单调迭代方法构造了一列单调的解序列, 然后证明其极限存在,并为原方程的解.并值得一提的是,这里的生成元g既可以关于变量y不连续,同时g关于变量y和z的变换范围也可以与时间参数t有关.

关键词: 倒向随机微分方程, 广义左Lipschitz条件, 存在性, 倒向随机微分方程, 广义左Lipschitz条件, 存在性

Abstract: In this paper, we proved the existence of the solution to a backward stochastic differential equations (BSDE) with the generator satisfying the generalized left-Lipschitz condition. The key idea for dealing with the problem consists in constructing a monotonic sequence of solutions to BSDE and then passing to the
limit. We construct a monotonic sequence of solutions by monotonic iteration technique. It is worth noting that the generator may be not continuous with respect to variable yand the varying of generator with respect to variables y and z may be not uniformly with respect to time parameter t.

Key words: existence, generalized left-Lipschitz, existence

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