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Asymptotic Results for First-Passage Times of Some Exponential Processes
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SYSNO ASEP 0498571 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název Asymptotic Results for First-Passage Times of Some Exponential Processes Tvůrce(i) D´Onofrio, Giuseppe (FGU-C)
Macci, C. (IT)
Pirozzi, E. (IT)Zdroj.dok. Methodology and Computing in Applied Probability. - : Springer - ISSN 1387-5841
Roč. 20, č. 4 (2018), s. 1453-1476Poč.str. 24 s. Jazyk dok. eng - angličtina Země vyd. US - Spojené státy americké Klíč. slova compound poisson proces ; large deviations ; moderate deviations ; normal approximation ; neuronal model Vědní obor RIV BB - Aplikovaná statistika, operační výzkum Obor OECD Statistics and probability CEP GA17-06943S GA ČR - Grantová agentura ČR Institucionální podpora FGU-C - RVO:67985823 UT WOS 000449431800021 EID SCOPUS 85052223603 DOI https://doi.org/10.1007/s11009-018-9659-7 Anotace 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. Pracoviště Fyziologický ústav Kontakt Lucie Trajhanová, lucie.trajhanova@fgu.cas.cz, Tel.: 241 062 400 Rok sběru 2019
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