ASYMPTOTIC EXPANSION of the DENSITY for HYPOELLIPTIC ROUGH DIFFERENTIAL EQUATION

Yuzuru Inahama, Nobuaki Naganuma

    Research output: Contribution to journalArticlepeer-review

    Abstract

    We study a rough differential equation driven by fractional Brownian motion with Hurst parameter <![CDATA[(1/4. 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.

    Original languageEnglish
    Pages (from-to)11-41
    Number of pages31
    JournalNagoya Mathematical Journal
    Volume243
    DOIs
    Publication statusPublished - Sept 2021

    All Science Journal Classification (ASJC) codes

    • General Mathematics

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