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

Blower, Gordon and Bolley, Francois (2006) Concentration of measure on product spaces with applications to Markov processes. Studia Mathematica, 175 (1). pp. 47-72. ISSN 0039-3223

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    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.

    Item Type: Article
    Journal or Publication Title: Studia Mathematica
    Additional Information: AMS 2000 classification: 60E15; 60E05; 39B62
    Uncontrolled Keywords: logarithmic Sobolev inequality ; optimal transportation
    Subjects: Q Science > QA Mathematics
    Departments: Faculty of Science and Technology > Mathematics and Statistics
    ID Code: 1694
    Deposited By: Professor Gordon Blower
    Deposited On: 18 Feb 2008 09:59
    Refereed?: Yes
    Published?: Published
    Last Modified: 15 Nov 2013 10:50
    Identification Number:
    URI: http://eprints.lancs.ac.uk/id/eprint/1694

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