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 |
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Pages (from-to) | 535-577 |
Number of pages | 43 |
Journal | Journal of the Mathematical Society of Japan |
Volume | 68 |
Issue number | 2 |
DOIs | |
Publication status | Published - Jan 1 2016 |
All Science Journal Classification (ASJC) codes
- Mathematics(all)