Generalized delay BSDE driven by fractional Brownian motion

Abstract

Abstract This paper deals with a class of Generalized delay backward 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} ). In this type of equation, a generator at time t can depend not only on the present but also the past solutions. We essentially establish existence and uniqueness of a solution in the case of Lipschitz coefficients. This paper is an extension of the first paper from [S. Aidara and I. Sane, Deplay BSDEs driven by fractional Brownian motion, Random Oper. Stoch. Equ. 30 2022, 1, 21–31]. The stochastic integral used throughout this paper is the divergence-type integral.