12,000

We have over 12,000 students, from over 100 countries, within one of the safest campuses in the UK

93%

93% of Lancaster students go into work or further study within six months of graduating

Home > Research > Publications & Outputs > Concentration of measure on product spaces with...
View graph of relations

« Back

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

Research output: Contribution to journalJournal article

Published

Journal publication date2006
JournalStudia Mathematica
Journal number1
Volume175
Number of pages26
Pages47-72
Original languageEnglish

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.

Bibliographic note

AMS 2000 classification: 60E15; 60E05; 39B62