Existence of density for solutions of mixed stochastic equations

Abstract

We consider a mixed stochastic differential equation $d{X}_t=a(t,X_t)dt+b(t,X_t)d{W}_t+c(t,X_t)d{B}_t^H$ 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.