文献类型：期刊文献

中文题名：Existence and Uniqueness of the Nonlinear BSDEs with a Small Parameter under Locally Lipschitz Condition

英文题名：Existence and Uniqueness of the Nonlinear BSDEs with a Small Parameter under Locally Lipschitz Condition

作者：XIE Zhen-yun[1];XIA Ning-mao[2]

机构：[1].Department of Applied Mathematics, Donghua University, Shanghai 201620, China;[2]Department of Mathematics, East China University of Science and Technology, Shanghai 200237, China

年份：2010

卷号：25

期号：3

起止页码：344

中文期刊名：Chinese Quarterly Journal of Mathematics

外文期刊名：数学季刊（英文版）

收录：CSTPCD;;CSCD:【CSCD2011_2012】；

基金：Supported by the NSFC(10901033)

语种：英文

中文关键词：nonlinear BSDE; locally Lipschitz condition; a small parameter

外文关键词：非线性的 BSDE；局部地 Lipschitz 状况；一个小参数；

摘要：In this paper we study the following nonlinear BSDE：y（t） ＋ ∫1 t f（s,y（s）,z（s））ds ＋ ∫1 t [z（s） ＋ g 1 （s,y（s）） ＋ εg 2 （s,y（s）,z（s））]dW s=ξ,t ∈ [0,1],where ε is a small parameter.The coefficient f is locally Lipschitz in y and z,the coefficient g 1 is locally Lipschitz in y,and the coefficient g 2 is uniformly Lipschitz in y and z.Let L N be the locally Lipschitz constant of the coefficients on the ball B（0,N） of R d × R d×r.We prove the existence and uniqueness of the solution when L N ～ √ log N and the parameter ε is small.
In this paper we study the following nonlinear BSDE:y(t)+∫1t f(s,y(s),z(s))ds+∫1t[z(s)+g1(s,y(s))+εg2(s,y(s),z(s))]dWs = ξ,t ∈[0,1],where ε is a small parameter.The coefficient f is locally Lipschitz in y and z,the coefficient g1 is locally Lipschitz in y,and the coefficient g2 is uniformly Lipschitz in y and z.Let LN be the locally Lipschitz constant of the coefficients on the ball B(O,N)of Ra × Ra×r.We prove the existence and uniqueness of the solution when LN～ √log N and the parameter εis small.