ON THE EXIT TIME FROM OPEN SETS OF SOME SEMI-MARKOV PROCESSES

• 成果类型: Article
• 署名作者: Ascione, Giacomo; Pirozzi, Enrica; Toaldo, Bruno
• 署名单位: University of Naples Federico II; University of Turin
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/19-AAP1525
• 发表日期: 2020
• 页码: 1130-1163
• 关键词: random-walks; diffusion; MODEL; EQUATIONS; BEHAVIOR; motion

摘要

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.