Concentration of measure on product spaces with applications to Markov processes

• Autorzy: Gordon Blower , François Bolley
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 60E15: Inequalities; stochastic orderings
• 60E05: Distributions: general theory
• 39B62: Functional inequalities, including subadditivity, convexity, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2006
• Tom: 175
• Numer: 1
• Strony: 47-72

Daty

wydano

2006

Twórcy

autor

Gordon Blower

• Department of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, UK

autor

François Bolley

• École Normale Supérieure de Lyon, Umpa, 46 allée d'Italie, F-69364 Lyon Cedex 07, France
• Institut de mathématiques - LSP, Université Paul Sabatier, F-31062 Toulouse Cedex 9, France

Identyfikatory

DOI

10.4064/sm175-1-3