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.
"Short time kernel asymptotics for Young SDE by means of Watanabe distribution theory." J. Math. Soc. Japan 68 (2) 535 - 577, April, 2016. https://doi.org/10.2969/jmsj/06820535