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Crossing and comparison of regenerative processes

Crossing and comparison of regenerative processes A method for a quantitative comparison of wide sense regenerative processes is discussed. The main idea appears to be to make assumptions on the processes being studied that permit one to construct so-called crossing times which are simultaneous regeneration times for another pair of regenerative processes (called crossing), each element of the pair coinciding in distribution with one of the initial processes. Provided that intercrossing times have proper moments (higher, than of the first order), the problem of uniform-in-time comparison is reduced (using renewal-type arguments) to obtaining comparison estimates over finite horizons only. Respective estimates are formulated in terms of probability metrics. Possible applications include continuity of queues, approximation of Markov chains, etc. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

Crossing and comparison of regenerative processes

Acta Applicandae Mathematicae , Volume 34 (2) – Dec 31, 2004

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References (22)

Publisher
Springer Journals
Copyright
Copyright
Subject
Mathematics; Computational Mathematics and Numerical Analysis; Applications of Mathematics; Partial Differential Equations; Probability Theory and Stochastic Processes; Calculus of Variations and Optimal Control; Optimization
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1007/BF00994263
Publisher site
See Article on Publisher Site

Abstract

A method for a quantitative comparison of wide sense regenerative processes is discussed. The main idea appears to be to make assumptions on the processes being studied that permit one to construct so-called crossing times which are simultaneous regeneration times for another pair of regenerative processes (called crossing), each element of the pair coinciding in distribution with one of the initial processes. Provided that intercrossing times have proper moments (higher, than of the first order), the problem of uniform-in-time comparison is reduced (using renewal-type arguments) to obtaining comparison estimates over finite horizons only. Respective estimates are formulated in terms of probability metrics. Possible applications include continuity of queues, approximation of Markov chains, etc.

Journal

Acta Applicandae MathematicaeSpringer Journals

Published: Dec 31, 2004

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