Ivan Nourdin
Published 2005-11-01, updated 2007-10-18Version 4
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.
Exact rate of convergence of some approximation schemes associated to SDEs driven by a fractional Brownian motion
Stochastic differential equations with non-negativity constraints driven by fractional Brownian motion
From constructive field theory to fractional stochastic calculus. (II) Constructive proof of convergence for the Lévy area of fractional Brownian motion with Hurst index $α\in(1/8,1/4)$
![QR code for arXiv:math/0511027 [math.PR]](http://oss.arxitics.com/images/favicon.svg)