Backward doubly stochastic differential equations driven by fractional Brownian motion with stochastic integral-Lipschitz coefficients

Abstract

Abstract This paper deals with a class of backward doubly stochastic differential equations driven by fractional Brownian motion with Hurst parameter H greater than 1 2 {\frac{1}{2}} . We essentially establish the existence and uniqueness of a solution in the case of stochastic Lipschitz coefficients and stochastic integral-Lipschitz coefficients. The stochastic integral used throughout the paper is the divergence-type integral.