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

Yuzuru Inahama

doi:10.2969/jmsj/06820535

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

Yuzuru Inahama

Department of Mathematical Sciences

Research output: Contribution to journal › Article

2 Citations (Scopus)

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 language	English
Pages (from-to)	535-577
Number of pages	43
Journal	Journal of the Mathematical Society of Japan
Volume	68
Issue number	2
DOIs	https://doi.org/10.2969/jmsj/06820535
Publication status	Published - Jan 1 2016

All Science Journal Classification (ASJC) codes

Mathematics(all)

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Inahama, Y. (2016). Short time kernel asymptotics for Young SDE by means of Watanabe distribution theory. Journal of the Mathematical Society of Japan, 68(2), 535-577. https://doi.org/10.2969/jmsj/06820535

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