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 - Jan 1 2016

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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