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Measure concentration for a class of random processes
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  • Published: March 1998

Measure concentration for a class of random processes

  • Katalin Marton1 

Probability Theory and Related Fields volume 110, pages 427–439 (1998)Cite this article

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Summary.

Let X={X i } i =−∞ ∞ be a stationary random process with a countable alphabet and distribution q. Let q ∞(·|x − k 0) denote the conditional distribution of X ∞=(X 1,X 2,…,X n ,…) given the k-length past:

Write d(1,x 1)=0 if 1=x 1, and d(1,x 1)=1 otherwise. We say that the process X admits a joining with finite distance u if for any two past sequences − k 0=(− k +1,…,0) and x − k 0=(x − k +1,…,x 0), there is a joining of q ∞(·|− k 0) and q ∞(·|x − k 0), say dist(0 ∞,X 0 ∞|− k 0,x − k 0), such that

The main result of this paper is the following inequality for processes that admit a joining with finite distance:

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Authors and Affiliations

  1. Mathematical Institute of the Hungarian Academy of Sciences, P.O. Box 127, H-1364 Budapest, Hungary e-mail: marton@math-inst.hu, , , , , , HU

    Katalin Marton

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  1. Katalin Marton
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Received: 6 May 1996 / In revised form: 29 September 1997

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Marton, K. Measure concentration for a class of random processes. Probab Theory Relat Fields 110, 427–439 (1998). https://doi.org/10.1007/s004400050154

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  • Issue Date: March 1998

  • DOI: https://doi.org/10.1007/s004400050154

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  • Mathematics Subject Classification (1991): 60F10
  • 60G10
  • 60J10
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