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 <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mfrac> <m:mn>1</m:mn> <m:mn>2</m:mn> </m:mfrac> </m:math> {\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.