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Asymptotic Results for First-Passage Times of Some Exponential Processes

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. 1453-1476
Number 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

Number of the records: 1