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September 2012 Piecewise-deterministic Markov processes as limits of Markov jump processes
Uwe Franz, Volkmar Liebscher, Stefan Zeiser
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Adv. in Appl. Probab. 44(3): 729-748 (September 2012). DOI: 10.1239/aap/1346955262

Abstract

A classical result about Markov jump processes states that a certain class of dynamical systems given by ordinary differential equations are obtained as the limit of a sequence of scaled Markov jump processes. This approach fails if the scaling cannot be carried out equally across all entities. In the present paper we present a convergence theorem for such an unequal scaling. In contrast to an equal scaling the limit process is not purely deterministic but still possesses randomness. We show that these processes constitute a rich subclass of piecewise-deterministic processes. Such processes apply in molecular biology where entities often occur in different scales of numbers.

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Uwe Franz. Volkmar Liebscher. Stefan Zeiser. "Piecewise-deterministic Markov processes as limits of Markov jump processes." Adv. in Appl. Probab. 44 (3) 729 - 748, September 2012. https://doi.org/10.1239/aap/1346955262

Information

Published: September 2012
First available in Project Euclid: 6 September 2012

zbMATH: 1254.60031
MathSciNet: MR3024607
Digital Object Identifier: 10.1239/aap/1346955262

Subjects:
Primary: 60F15
Secondary: 60J28, 92C40

Rights: Copyright © 2012 Applied Probability Trust

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Vol.44 • No. 3 • September 2012
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