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Random time-changes and asymptotic results for a class of continuous-time Markov chains on integers with alternating rates
Volume 8, Issue 1 (2021), pp. 63–91
Luisa Beghin ORCID icon link to view author Luisa Beghin details   Claudio Macci ORCID icon link to view author Claudio Macci details   Barbara Martinucci ORCID icon link to view author Barbara Martinucci details  

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https://doi.org/10.15559/20-VMSTA169
Pub. online: 21 December 2020      Type: Research Article      Open accessOpen Access

Received
3 September 2020
Revised
12 November 2020
Accepted
4 December 2020
Published
21 December 2020

Abstract

We consider continuous-time Markov chains on integers which allow transitions to adjacent states only, with alternating rates. This kind of processes are useful in the study of chain molecular diffusions. We give explicit formulas for probability generating functions, and also for means, variances and state probabilities of the random variables of the process. Moreover we study independent random time-changes with the inverse of the stable subordinator, the stable subordinator and the tempered stable subordinator. We also present some asymptotic results in the fashion of large deviations. These results give some generalizations of those presented in [Journal of Statistical Physics 154 (2014), 1352–1364].

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Keywords
Large deviations moderate deviations fractional process tempered stable subordinator

MSC2010
60F10 60J27 60G22 60G52

Funding
Luisa Beghin acknowledges the support of INDAM-GNAMPA. Claudio Macci acknowledges the support of: MIUR Excellence Department Project awarded to the Department of Mathematics, University of Rome Tor Vergata (CUP E83C18000100006); Indam-GNAMPA (research project “Stime asintotiche: principi di invarianza e grandi deviazioni”). Barbara Martinucci acknowledges the support of: MIUR–PRIN 2017, Project “Stochastic Models for Complex Systems” (no. 2017JFFHSH); INDAM-GNCS.

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