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

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

2011-07-19

arxiv.org/abs/1107.3790v1

Statistics and Probability letters 81(2011)

Mathematics

Probability

Scientific paper

Given a fractional Brownian motion \,\,$(B_{t}^{H})_{t\geq 0}$,\, with Hurst parameter \,$> 1/2$\,\,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.

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