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Asymptotic Results for First-Passage Times of Some Exponential Processes
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SYSNO ASEP 0498571 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Asymptotic Results for First-Passage Times of Some Exponential Processes Author(s) D´Onofrio, Giuseppe (FGU-C)
Macci, C. (IT)
Pirozzi, E. (IT)Source Title Methodology and Computing in Applied Probability. - : Springer - ISSN 1387-5841
Roč. 20, č. 4 (2018), s. 1453-1476Number of pages 24 s. Language eng - English Country US - United States Keywords compound poisson proces ; large deviations ; moderate deviations ; normal approximation ; neuronal model Subject RIV BB - Applied Statistics, Operational Research OECD category Statistics and probability R&D Projects GA17-06943S GA ČR - Czech Science Foundation (CSF) Institutional support FGU-C - RVO:67985823 UT WOS 000449431800021 EID SCOPUS 85052223603 DOI 10.1007/s11009-018-9659-7 Annotation We consider the process {V (t) : t 0} defined by V (t) = v(0)e(X(t)) (for all t 0), where v(0) >0 and {X(t) : t 0} is a compound Poisson process with exponentially distributed jumps and a negative drift. This process can be seen as the neuronal membrane potential in the stochastic model for the firing activity of a neuronal unit presented in Di Crescenzo and Martinucci (Math Biosci 209(2):547-563 2007). We also consider the process (for all t 0) and is the Normal approximation (as) of the process {X(t) : t 0}. In this paper we are interested in the first-passage times through a constant firing threshold (where > v(0)) for both processes {V (t) : t 0} and in the fashion of large deviations. We also study some statistical applications for both models, with some numerical evaluations and simulation results. Workplace Institute of Physiology Contact Lucie Trajhanová, lucie.trajhanova@fgu.cas.cz, Tel.: 241 062 400 Year of Publishing 2019
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