Short time kernel asymptotics for Young SDE by means of Watanabe distribution theory

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    Abstract

    In this paper we study short time asymptotics of a density function of the solution of a stochastic differential equation driven by fractional Brownian motion with Hurst parameter H (1/2 < H < 1) when the coefficient vector fields satisfy an ellipticity condition at the starting point. We prove both on-diagonal and off-diagonal asymptotics under mild additional assumptions. Our main tool is Malliavin calculus, in particular, Watanabe's theory of generalized Wiener functionals.

    Original languageEnglish
    Pages (from-to)535-577
    Number of pages43
    JournalJournal of the Mathematical Society of Japan
    Volume68
    Issue number2
    DOIs
    Publication statusPublished - 2016

    All Science Journal Classification (ASJC) codes

    • Mathematics(all)

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