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.
基金
Supported by the NSFC(10901033)