English

A linear stochastic differential equation driven by a fractional Brownian motion with Hurst parameter >1/2

Probability 2011-07-20 v1

Abstract

Given a fractional Brownian motion \,\,(BtH)t0(B_{t}^{H})_{t\geq 0},\, with Hurst parameter \,>1/2> 1/2\,\,we study the properties of all solutions of \,\,: {equation} X_{t}=B_{t}^{H}+\int_0^t X_{u}d\mu(u), \;\; 0\leq t\leq 1{equation} A different stochastic calculus is required for the process because it is not a semimartingale.

Keywords

Cite

@article{arxiv.1107.3790,
  title  = {A linear stochastic differential equation driven by a fractional Brownian motion with Hurst parameter >1/2},
  author = {Mamadou Abdoul Diop and Youssef Ouknine},
  journal= {arXiv preprint arXiv:1107.3790},
  year   = {2011}
}
R2 v1 2026-06-21T18:39:01.173Z