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

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

2011-10-12

arxiv.org/abs/1110.2604v1

Mathematics

Probability

47 pages, no figure

Scientific paper

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 $H \in (1/2, 1)$ 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.

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