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June 2020 On the exit time from open sets of some semi-Markov processes
Giacomo Ascione, Enrica Pirozzi, Bruno Toaldo
Ann. Appl. Probab. 30(3): 1130-1163 (June 2020). DOI: 10.1214/19-AAP1525

Abstract

In this paper we characterize the distribution of the first exit time from an arbitrary open set for a class of semi-Markov processes obtained as time-changed Markov processes. We estimate the asymptotic behaviour of the survival function (for large $t$) and of the distribution function (for small $t$) and we provide some conditions for absolute continuity. We have been inspired by a problem of neurophyshiology and our results are particularly usefull in this field, precisely for the so-called Leaky Integrate-and-Fire (LIF) models: the use of semi-Markov processes in these models appear to be realistic under several aspects, for example, it makes the intertimes between spikes a r.v. with infinite expectation, which is a desiderable property. Hence, after the theoretical part, we provide a LIF model based on semi-Markov processes.

Citation

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Giacomo Ascione. Enrica Pirozzi. Bruno Toaldo. "On the exit time from open sets of some semi-Markov processes." Ann. Appl. Probab. 30 (3) 1130 - 1163, June 2020. https://doi.org/10.1214/19-AAP1525

Information

Received: 1 March 2019; Revised: 1 August 2019; Published: June 2020
First available in Project Euclid: 29 July 2020

MathSciNet: MR4133370
Digital Object Identifier: 10.1214/19-AAP1525

Subjects:
Primary: 60G40, 60K15
Secondary: 60G51

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.30 • No. 3 • June 2020
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