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

Chinese Quarterly Journal of Mathematics ›› 2010, Vol. 25 ›› Issue (3): 344-351.

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)；

Abstract

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

CLC Number:

O211.63

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

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