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arXiv · 1902.05219

Asymptotic expansion of the density for hypoelliptic rough differential equation

Yuzuru Inahama·Nobuaki Naganuma
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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.

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Yuzuru Inahama, Nobuaki Naganuma. 2019-02-14. Asymptotic expansion of the density for hypoelliptic rough differential equation. https://arxiv.org/abs/1902.05219

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