HAL: hal-00138773, version 2

arXiv: math/0703794

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v1 (2007-03-27)

v2 (2007-09-28)

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

Sébastien Darses 1, Ivan Nourdin 1

(2007-03-27)

We study the asymptotic developments with respect to $h$ of E[D_h f(X_t)], E[D_h f(X_t)|F_t] and E[D_h f(X_t)|X_t], where D_h f(X_t)=f(X_{t+h})-f(X_t), when f:R->R is a smooth real function, t is a fixed time, X is the solution of a one-dimensional stochastic differential equation driven by a fractional Brownian motion of Hurst index H>1/2 and F is its natural filtration.

1:	Laboratoire de Probabilités et Modèles Aléatoires (LPMA)
	CNRS : UMR7599 – Université Pierre et Marie Curie (UPMC) - Paris VI – Université Paris VII - Paris Diderot

Subject

:

Mathematics/Probability

Keyword(s): Asymptotic development – Fractional Brownian motion – stochastic differential equation – Malliavin calculus

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From: Ivan Nourdin <>

Submitted on: Thursday, 27 September 2007 20:41:22

Updated on: Friday, 28 September 2007 09:13:00