Abstract
We study a stochastic differential equation in the sense of rough path theory driven by fractional Brownian rough path with Hurst parameter $H ~(1/3 < H \le 1/2)$ 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.
Citation
Yuzuru Inahama. "Short time kernel asymptotics for rough differential equation driven by fractional Brownian motion." Electron. J. Probab. 21 1 - 29, 2016. https://doi.org/10.1214/16-EJP4144
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