Asymptotic Results for First-Passage Times of Some Exponential Processes
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985823%3A_____%2F18%3A00498571" target="_blank" >RIV/67985823:_____/18:00498571 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s11009-018-9659-7" target="_blank" >http://dx.doi.org/10.1007/s11009-018-9659-7</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s11009-018-9659-7" target="_blank" >10.1007/s11009-018-9659-7</a>
Alternative languages
Result language
angličtina
Original language name
Asymptotic Results for First-Passage Times of Some Exponential Processes
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10103 - Statistics and probability
Result continuities
Project
<a href="/en/project/GA17-06943S" target="_blank" >GA17-06943S: Neural coding precision and its adaptation to the stimulus statistics</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Methodology and Computing in Applied Probability
ISSN
1387-5841
e-ISSN
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Volume of the periodical
20
Issue of the periodical within the volume
4
Country of publishing house
US - UNITED STATES
Number of pages
24
Pages from-to
1453-1476
UT code for WoS article
000449431800021
EID of the result in the Scopus database
2-s2.0-85052223603