Short time kernel asymptotics for Young SDE by means of Watanabe distribution theory

Abstract

In this paper we study short time asymptotics of a density function of the solution of a stochastic differential equation driven by fractional Brownian motion with Hurst parameter $H$ (1/2 < $H$ < 1) when the coefficient vector fields satisfy an ellipticity condition at the starting point. We prove both on-diagonal and off-diagonal asymptotics under mild additional assumptions. Our main tool is Malliavin calculus, in particular, Watanabe's theory of generalized Wiener functionals.