A linear stochastic differential equation driven by a fractional Brownian motion with Hurst parameter >1/2
Abstract
Given a fractional Brownian motion \,\,(BtH)t≥ 0,\, with Hurst parameter \,> 1/2\,\,we study the properties of all solutions of \,\,: equation Xt=BtH+∫0t Xudμ(u), \;\; 0≤ t≤ 1equation A different stochastic calculus is required for the process because it is not a semimartingale.
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