带小参数的非线性倒向随机微分议程在局部Lipschitz条件下解的存在唯一性

数学季刊 ›› 2010, Vol. 25 ›› Issue (3): 344-351.

带小参数的非线性倒向随机微分议程在局部Lipschitz条件下解的存在唯一性

1. Department of Applied Mathematics, Donghua University2. Department of Mathematics, East China University of Science and Technology

收稿日期:2006-10-25 出版日期:2010-09-30 发布日期:2023-05-24
作者简介:XIE Zhen-yun(1980- ), male, native of Shanghai, Ph.D., engages in stochastic analysis and applications; XIA Ning-mao(1944- ), male, native of Shanghai, a professor of East China University of Science and Technology, engages in stochastic analysis applications.
基金资助:
Supported by the NSFC(10901033)；

Existence and Uniqueness of the Nonlinear BSDEs with a Small Parameter under Locally Lipschitz Condition

1. Department of Applied Mathematics, Donghua University2. Department of Mathematics, East China University of Science and Technology

Received:2006-10-25 Online:2010-09-30 Published:2023-05-24
About author:XIE Zhen-yun(1980- ), male, native of Shanghai, Ph.D., engages in stochastic analysis and applications; XIA Ning-mao(1944- ), male, native of Shanghai, a professor of East China University of Science and Technology, engages in stochastic analysis applications.
Supported by:
Supported by the NSFC(10901033)；

摘要/Abstract

摘要： In this paper we study the following nonlinear BSDE: y(t) +... , 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 ～√ logN and the parameter ε is small.

关键词: nonlinear BSDE, locally Lipschitz condition, a small parameter

Abstract: In this paper we study the following nonlinear BSDE: y(t) +... , 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 ～√ logN and the parameter ε is small.

Key words: nonlinear BSDE, locally Lipschitz condition, a small parameter

中图分类号:

O211.63

谢臻赟, 夏宁茂. 带小参数的非线性倒向随机微分议程在局部Lipschitz条件下解的存在唯一性[J]. 数学季刊, 2010, 25(3): 344-351.

XIE Zhen-yun, XIA Ning-mao. Existence and Uniqueness of the Nonlinear BSDEs with a Small Parameter under Locally Lipschitz Condition[J]. Chinese Quarterly Journal of Mathematics, 2010, 25(3): 344-351.

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