Linear Stochastic Differential Equations Driven by a Fractional Brownian Motion with Hurst Parameter less than 1/2
Probability
2007-06-13 v1 Statistics Theory
Statistics Theory
Abstract
In this paper we use the chaos decomposition approach to establish the existence of a unique continuous solution to linear fractional differential equations of the Skorohod type. Here the coefficients are deterministic, the inital condition is anticipating and the underlying fractional Brownian motion has Hurst parameter less than 1/2. We provide an explicit expression for the chaos decomposition of the solution in order to show our results.
Cite
@article{arxiv.math/0603636,
title = {Linear Stochastic Differential Equations Driven by a Fractional Brownian Motion with Hurst Parameter less than 1/2},
author = {Jorge A. Leon and Jaime San Martin},
journal= {arXiv preprint arXiv:math/0603636},
year = {2007}
}