Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Concentration of measure on product spaces with applications to Markov processes.
AU - Blower, Gordon
AU - Bolley, Francois
N1 - AMS 2000 classification: 60E15; 60E05; 39B62
PY - 2006
Y1 - 2006
N2 - 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 and transportation inequalities. In the case of Euclidean space, there are sufficient conditions for the joint law to satisfy a logarithmic Sobolev inequality. In several cases, the constants obtained are of optimal 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 and weakly dependent random variabels under Dobrushkin--Shlosman type conditions. The paper also contains applications to Markov processes including the ARMA process.
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 and transportation inequalities. In the case of Euclidean space, there are sufficient conditions for the joint law to satisfy a logarithmic Sobolev inequality. In several cases, the constants obtained are of optimal 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 and weakly dependent random variabels under Dobrushkin--Shlosman type conditions. The paper also contains applications to Markov processes including the ARMA process.
KW - logarithmic Sobolev inequality
KW - optimal transportation
U2 - 10.4064/sm175-1-3
DO - 10.4064/sm175-1-3
M3 - Journal article
VL - 175
SP - 47
EP - 72
JO - Studia Mathematica
JF - Studia Mathematica
SN - 0039-3223
IS - 1
ER -