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Continuity of random sequences and approximation of Markov chains

Published online by Cambridge University Press:  01 July 2016

V. V. Kalashnikov  and
S. A. Anichkin
V. V. Kalashnikov*
Affiliation:
Institute for Systems Studies
S. A. Anichkin*
Affiliation:
Moscow Physico-Technical Institute
*
∗Postal address: Institute for Systems Studies, 29 Ryleyev St., 119034 Moscow, U.S.S.R.
∗∗Postal address: Department of Applied Mathematics and Control, Moscow Physico-Technical Institute, 141700 g. Dolgoprudnyi, U.S.S.R.
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Abstract

We derive conditions for the time-uniform continuity of random sequences with respect to variations of governing parameters, and also obtain some estimates of the modulus of continuity. We then apply the results to find conditions of continuity for Markov chains with arbitrary state space, and to construct finite approximations to them.

Keywords

MARKOV CHAINSCONTINUITYMETRICESTIMATECOMPACTNESSWEAK CONVERGENCE
Type
Research Article
Information
Advances in Applied Probability , Volume 13 , Issue 2 , June 1981 , pp. 402 - 414
Copyright
Copyright © Applied Probability Trust 1981 

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