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ASYMPTOTIC EXPANSION OF THE DENSITY FOR HYPOELLIPTIC ROUGH DIFFERENTIAL EQUATION

  • YUZURU INAHAMA (a1) and NOBUAKI NAGANUMA (a2)

Abstract

We study a rough differential equation driven by fractional Brownian motion with Hurst parameter $H$ $(1/4<H\leqslant 1/2)$ . Under Hörmander’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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The first author was partially supported by JSPS KAKENHI Grant Number JP15K04922. The second author was partially supported by JSPS KAKENHI Grant Number JP17K14202.

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ASYMPTOTIC EXPANSION OF THE DENSITY FOR HYPOELLIPTIC ROUGH DIFFERENTIAL EQUATION

  • YUZURU INAHAMA (a1) and NOBUAKI NAGANUMA (a2)

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