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

@article{Georgiou2021BoundsFM,
title={Bounds for mixing times for finite semi-Markov processes with heavy-tail jump distribution},
author={Nicos Georgiou and Enrico Scalas},
journal={Fractional Calculus and Applied Analysis},
year={2021},
volume={25},
pages={229-243}
}
• Published 16 November 2021
• Mathematics
• Fractional Calculus and Applied Analysis
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 $$\beta$$ β . We then focus on $$\beta \in (0,1)$$ β ∈ ( 0 , 1 ) , leading to infinite expectation for inter-arrival times…
2 Citations
A complex fractional derivative can be derived by formally extending the integer k in the k th derivative of a function, computed via Cauchy’s integral, to complex α . This straightforward approach

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