backward stochastic differential equations driven by both standard and
fractional Brownian motions with time deplayed generators
Abstract
This paper deals with a class of backward stochastic differential
equations driven by both standard and fractional Brownian motions with
time deplayed generators. In this type of equation, a generator at time
$t$ can depend on the values of a solution in the past, weighted with
a time delay function, for instance, of the moving average type. We
establish an existence and uniqueness result of solutions for a
sufficiently small time horizon or for a sufficiently small Lipschitz
constant of a generator.