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Concentration of measure on product spaces with applications to Markov processes.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

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Concentration of measure on product spaces with applications to Markov processes. / Blower, Gordon; Bolley, Francois.
In: Studia Mathematica, Vol. 175, No. 1, 2006, p. 47-72.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Blower, G & Bolley, F 2006, 'Concentration of measure on product spaces with applications to Markov processes.', Studia Mathematica, vol. 175, no. 1, pp. 47-72. https://doi.org/10.4064/sm175-1-3

APA

Blower, G., & Bolley, F. (2006). Concentration of measure on product spaces with applications to Markov processes. Studia Mathematica, 175(1), 47-72. https://doi.org/10.4064/sm175-1-3

Vancouver

Blower G, Bolley F. Concentration of measure on product spaces with applications to Markov processes. Studia Mathematica. 2006;175(1):47-72. doi: 10.4064/sm175-1-3

Author

Blower, Gordon ; Bolley, Francois. / Concentration of measure on product spaces with applications to Markov processes. In: Studia Mathematica. 2006 ; Vol. 175, No. 1. pp. 47-72.

Bibtex

@article{671fb93b30214ec3a2c6b5faea51b3e8,
title = "Concentration of measure on product spaces with applications to Markov processes.",
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 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.",
keywords = "logarithmic Sobolev inequality, optimal transportation",
author = "Gordon Blower and Francois Bolley",
note = "AMS 2000 classification: 60E15; 60E05; 39B62",
year = "2006",
doi = "10.4064/sm175-1-3",
language = "English",
volume = "175",
pages = "47--72",
journal = "Studia Mathematica",
issn = "0039-3223",
publisher = "Instytut Matematyczny",
number = "1",

}

RIS

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 -