Asymptotic Results for First-Passage Times of Some Exponential Processes

0498571 - FGÚ 2019 RIV US eng J - Journal Article
D´Onofrio, Giuseppe - Macci, C. - Pirozzi, E.
Asymptotic Results for First-Passage Times of Some Exponential Processes.
Methodology and Computing in Applied Probability. Roč. 20, č. 4 (2018), s. 1453-1476. ISSN 1387-5841. E-ISSN 1573-7713
R&D Projects: GA ČR(CZ) GA17-06943S
Institutional support: RVO:67985823
Keywords : compound poisson proces * large deviations * moderate deviations * normal approximation * neuronal model
OECD category: Statistics and probability
Impact factor: 0.746, year: 2018

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.
Permanent Link: http://hdl.handle.net/11104/0290898