Concentration of measure on product spaces with applications to Markov processes

Gordon Blower, and François Bolley. "Concentration of measure on product spaces with applications to Markov processes." Studia Mathematica 175.1 (2006): 47-72. <http://eudml.org/doc/285156>.

@article{GordonBlower2006,
abstract = {For a stochastic process with state space some Polish space, this paper gives sufficient conditions on the initial and conditional distributions for the joint law to satisfy Gaussian concentration inequalities and transportation inequalities. In the case of the Euclidean space $ℝ^\{m\}$, there are sufficient conditions for the joint law to satisfy a logarithmic Sobolev inequality. In several cases, the constants obtained are of optimal order of growth with respect to the number of random variables, or are independent of this number. These results extend results known for mutually independent random variables to weakly dependent random variables under Dobrushin-Shlosman type conditions. The paper also contains applications to Markov processes including the ARMA process.},
author = {Gordon Blower, François Bolley},
journal = {Studia Mathematica},
keywords = {logarithmic Sobolev inequality; optimal transportation},
language = {eng},
number = {1},
pages = {47-72},
title = {Concentration of measure on product spaces with applications to Markov processes},
url = {http://eudml.org/doc/285156},
volume = {175},
year = {2006},
}

TY - JOUR
AU - Gordon Blower
AU - François Bolley
TI - Concentration of measure on product spaces with applications to Markov processes
JO - Studia Mathematica
PY - 2006
VL - 175
IS - 1
SP - 47
EP - 72
AB - For a stochastic process with state space some Polish space, this paper gives sufficient conditions on the initial and conditional distributions for the joint law to satisfy Gaussian concentration inequalities and transportation inequalities. In the case of the Euclidean space $ℝ^{m}$, there are sufficient conditions for the joint law to satisfy a logarithmic Sobolev inequality. In several cases, the constants obtained are of optimal order of growth with respect to the number of random variables, or are independent of this number. These results extend results known for mutually independent random variables to weakly dependent random variables under Dobrushin-Shlosman type conditions. The paper also contains applications to Markov processes including the ARMA process.
LA - eng
KW - logarithmic Sobolev inequality; optimal transportation
UR - http://eudml.org/doc/285156
ER -