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

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

2012-02-29

arxiv.org/abs/1202.6558v1

Bernoulli 2012, Vol. 18, No. 1, 1-23

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.3150/10-BEJ324 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statisti

Scientific paper

10.3150/10-BEJ324

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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