Bounds for mixing times for finite semi-Markov processes with heavy-tail jump distribution

Georgiou, Nicos and Scalas, Enrico (2022) Bounds for mixing times for finite semi-Markov processes with heavy-tail jump distribution. Fractional Calculus and Applied Analysis, 25 (1). pp. 229-243. ISSN 1311-0454

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Abstract

Consider a Markov chain with finite state space and suppose you wish to change time replacing the integer step index n with a random counting process N(t). What happens to the mixing time of the Markov chain? We present a partial reply in a particular case of interest in which N(t) is a counting renewal process with power-law distributed inter-arrival times of index β. We then focus on β∈(0,1), leading to infinite expectation for inter-arrival times and further study the situation in which inter-arrival times follow the Mittag-Leffler distribution of order β.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Research Centres and Groups: Probability and Statistics Research Group
Subjects: Q Science > QA Mathematics > QA0273 Probabilities. Mathematical statistics > QA0274 Stochastic processes
Q Science > QA Mathematics > QA0273 Probabilities. Mathematical statistics > QA0274.7 Markov processes. Markov chains
Depositing User: Enrico Scalas
Date Deposited: 17 Nov 2021 09:54
Last Modified: 27 May 2022 13:30
URI: http://sro.sussex.ac.uk/id/eprint/102952

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