# 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} }

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…

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