Existence of Density for Solutions of Mixed Stochastic Equations

Abstract

We consider a mixed stochastic differential equation $d{X_t}=a(t,X_t)d{t}+b(t,X_t) d{W_t}+c(t,X_t)d{B^H_t}$ driven by independent multidimensional Wiener process and fractional Brownian motion. Under Hormander type conditions we show that the distribution of $X_t$ possesses a density with respect to the Lebesgue measure.