Transportation inequalities for stochastic differential equations driven by a fractional Brownian motion. (English) Zbl 1242.60056

Saussereau, Bruno

Bernoulli 18, No. 1, 1-23 (2012).

Summary: 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.

MSC:

60H10	Stochastic ordinary differential equations (aspects of stochastic analysis)
60E15	Inequalities; stochastic orderings

Keywords:

fractional Brownian motion; fractional calculus; stochastic differential equations; transportation inequalities

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