Asymptotic expansions at any time for scalar fractional SDEs with Hurst index $H>1/2$

Abstract

We study the asymptotic expansions with respect to $h$ of \[\mathrm{E}[Δ_hf(X_t)],\qquad \mathrm{E}[Δ_hf(X_t)|\mathscr{F}^X_t]\quadand\quad \mathrm{E}[Δ_hf(X_t)|X_t],\] where ${\Delta }_{h}f(X_t)=f(X_{t+h})-f(X_t)$, when $f:\mathbb{R}\to \mathbb{R}$ is a smooth real function, $t\ge 0$ is a fixed time, $X$ is the solution of a one-dimensional stochastic differential equation driven by a fractional Brownian motion with Hurst index $H>1/2$ and ${\mathcal{F}}^X$ is its natural filtration.

Published in at http://dx.doi.org/10.3150/08-BEJ124 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

References in corpus (1)

• Stochastic derivatives for fractional diffusions