JACOBI PROCESSES DRIVEN BY FRACTIONAL BROWNIAN MOTION

Abstract

In this paper we study a Jacobi equation driven by fractional Brownian motion with Hurst index $H\in (\frac{1}{2},1).$ We first prove the existence and uniqueness of the solution. Then we investigate Malliavin differentiability and smoothness of the density of the solution. Finally, we point out that the solution can be approximated by semimartingales.