Malliavin differentiability and regularity of densities in semi-linear stochastic delay equations driven by weighted fractional Brownian motion

Abstract

In this work, we will show the existence and uniqueness of the solution to semi-linear stochastic differential equations driven by weighted fractional Brownian motion with delay. We also prove smoothness of the density of the solution with respect to Lebesgue's measure on R d for d ≥ 1.