## Electronic Journal of Probability

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

Yuzuru Inahama

#### 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.

#### Article information

Source
Electron. J. Probab., Volume 21 (2016), paper no. 34, 29 pp.

Dates
Accepted: 28 March 2016
First available in Project Euclid: 22 April 2016

https://projecteuclid.org/euclid.ejp/1461332875

Digital Object Identifier
doi:10.1214/16-EJP4144

Mathematical Reviews number (MathSciNet)
MR3492938

Zentralblatt MATH identifier
1338.60142

#### Citation

Inahama, Yuzuru. Short time kernel asymptotics for rough differential equation driven by fractional Brownian motion. Electron. J. Probab. 21 (2016), paper no. 34, 29 pp. doi:10.1214/16-EJP4144. https://projecteuclid.org/euclid.ejp/1461332875

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