Asymptotic expansion of the density for hypoelliptic rough differential equation

Yuzuru Inahama; Nobuaki Naganuma

Asymptotic expansion of the density for hypoelliptic rough differential equation

Probability 2019-09-12 v2

Authors: Yuzuru Inahama , Nobuaki Naganuma

Abstract

We study a rough differential equation driven by fractional Brownian motion with Hurst parameter $H$ $(1/4<H \le 1/2)$ . Under H\"ormander's condition on the coefficient vector fields, the solution has a smooth density for each fixed time. Using Watanabe's distributional Malliavin calculus, we obtain a short time full asymptotic expansion of the density under quite natural assumptions. Our main result can be regarded as a "fractional version" of Ben Arous' famous work on the off-diagonal asymptotics.

Keywords

rough differential equation fractional brownian motion hypoelliptic density asymptotic expansion malliavin calculus hormander condition

Cite

@article{arxiv.1902.05219,
  title  = {Asymptotic expansion of the density for hypoelliptic rough differential equation},
  author = {Yuzuru Inahama and Nobuaki Naganuma},
  journal= {arXiv preprint arXiv:1902.05219},
  year   = {2019}
}

Comments

Typos were fixed

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