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

preprint2011arXivOpen access

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

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