Short time kernel asymptotics for rough differential equation driven by fractional Brownian motion
Probability
2016-03-29 v3
Abstract
We study a stochastic differential equation in the sense of rough path theory driven by fractional Brownian rough path with Hurst parameter H (1/3 < H <= 1/2) under the ellipticity assumption at the starting point. In such a case, the law of the solution at a fixed time has a kernel, i.e., a density function with respect to Lebesgue measure. In this paper we prove a short time off-diagonal asymptotic expansion of the kernel under mild additional assumptions. Our main tool is Watanabe's distributional Malliavin calculus.
Cite
@article{arxiv.1403.3181,
title = {Short time kernel asymptotics for rough differential equation driven by fractional Brownian motion},
author = {Yuzuru Inahama},
journal= {arXiv preprint arXiv:1403.3181},
year = {2016}
}
Comments
Revised and shortened version. 38 pages, no figure. arXiv admin note: text overlap with arXiv:1110.2604