Short time kernel asymptotics for rough differential equation driven by fractional Brownian motion

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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.

Original languageEnglish
Article number34
JournalElectronic Journal of Probability
Volume21
DOIs
Publication statusPublished - Jan 1 2016

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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