Small-time kernel expansion for solutions of stochastic differential equations driven by fractional Brownian motions

摘要

The goal of this paper is to show that under some assumptions, for a d-dimensional fractional Brownian motion with Hurst parameter H>12, the density of the solution of the stochastic differential equation Xtx=x+∑i=1d∫0tVi(Xsx)dBsi, admits the following asymptotics at small times: p(t;x,y)=1(tH)de-d2(x,y)2t2H(∑i=0Nci(x,y)t2iH+O(t2(N+1)H)).