A simple theory for the study of SDEs driven by a fractional Brownian motion, in dimension one - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year : 2007

A simple theory for the study of SDEs driven by a fractional Brownian motion, in dimension one

Abstract

In this paper, we will focus - in dimension one - on the SDEs of the type dX_t=s(X_t)dB_t+b(X_t)dt where B is a fractional Brownian motion. Our principal motivation is to describe one of the simplest theory - from our point of view - allowing to study this SDE, and this for any Hurst index H between 0 and 1. We will consider several definitions of solution and we will study, for each one of them, in which condition one has existence and uniqueness. Finally, we will examine the convergence or not of the canonical scheme associated to our SDE, when the integral with respect to fBm is defined using the Russo-Vallois symmetric integral.
Fichier principal
Vignette du fichier
nourdin.pdf (236.5 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-00012961 , version 1 (30-10-2005)
hal-00012961 , version 2 (04-11-2005)
hal-00012961 , version 3 (16-12-2005)
hal-00012961 , version 4 (25-01-2006)
hal-00012961 , version 5 (17-10-2007)

Identifiers

Cite

Ivan Nourdin. A simple theory for the study of SDEs driven by a fractional Brownian motion, in dimension one. 2007. ⟨hal-00012961v5⟩
200 View
662 Download

Altmetric

Share

Gmail Facebook X LinkedIn More