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

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
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### References:

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