Transportation inequalities for stochastic differential equations driven by a fractional Brownian motion

Bruno Saussereau

doi:10.3150/10-bej324

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arXiv · 1202.6558

Transportation inequalities for stochastic differential equations driven by a fractional Brownian motion

Bruno Saussereau

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Abstract

We establish Talagrand's $T_1$ and $T_2$ inequalities for the law of the solution of a stochastic differential equation driven by a fractional Brownian motion with Hurst parameter $H>1/2$. We use the $L^2$ metric and the uniform metric on the path space of continuous functions on $[0,T]$. These results are applied to study small-time and large-time asymptotics for the solutions of such equations by means of a Hoeffding-type inequality.

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Bruno Saussereau. 2012-02-29. Transportation inequalities for stochastic differential equations driven by a fractional Brownian motion. https://doi.org/10.3150/10-bej324

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