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

Bruno Saussereau

doi:10.3150/10-BEJ324

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

Statistics Theory 2012-03-01 v1 Statistics Theory

Authors: 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.

Keywords

transportation inequalities Talagrand inequalities stochastic differential equations fractional Brownian motion Hurst parameter Hoeffding inequality

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@article{arxiv.1202.6558,
  title  = {Transportation inequalities for stochastic differential equations driven by a fractional Brownian motion},
  author = {Bruno Saussereau},
  journal= {arXiv preprint arXiv:1202.6558},
  year   = {2012}
}

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Published in at http://dx.doi.org/10.3150/10-BEJ324 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

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

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