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Stationarity properties of neural networks

Asmussen, Sören LU and Turova, Tatyana LU (1998) In Journal of Applied Probability 35(4). p.783-794
Abstract
A neural model with N interacting neurons is considered. A firing of neuron i delays the firing times of all other neurons by the same random variable theta((i)), and in isolation the firings of the neuron occur according to a renewal process with generic interarrival time Y-(i). The stationary distribution of the N-vector of inhibitions at a firing time is computed, and involves waiting distributions of GI/G/1 queues and ladder height renewal processes. Further, the distribution of the period of activity of a neuron is studied for the symmetric case where theta((i)) and Y-(i) do not depend upon i. The tools are probabilistic and involve path decompositions, Palm theory and random walks.
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
inhibition, ladder height distribution, Palm theory, path decomposition, queuing theory, random walk, MARTINGALES, QUEUE, waiting time distribution, renewal process
in
Journal of Applied Probability
volume
35
issue
4
pages
783 - 794
publisher
Applied Probability Trust
external identifiers
  • scopus:0032250909
ISSN
1475-6072
language
English
LU publication?
yes
id
fc375721-454b-4a7f-acd5-34241daaab94 (old id 1273195)
date added to LUP
2008-12-09 14:04:00
date last changed
2017-01-01 07:38:24
@article{fc375721-454b-4a7f-acd5-34241daaab94,
  abstract     = {A neural model with N interacting neurons is considered. A firing of neuron i delays the firing times of all other neurons by the same random variable theta((i)), and in isolation the firings of the neuron occur according to a renewal process with generic interarrival time Y-(i). The stationary distribution of the N-vector of inhibitions at a firing time is computed, and involves waiting distributions of GI/G/1 queues and ladder height renewal processes. Further, the distribution of the period of activity of a neuron is studied for the symmetric case where theta((i)) and Y-(i) do not depend upon i. The tools are probabilistic and involve path decompositions, Palm theory and random walks.},
  author       = {Asmussen, Sören and Turova, Tatyana},
  issn         = {1475-6072},
  keyword      = {inhibition,ladder height distribution,Palm theory,path decomposition,queuing theory,random walk,MARTINGALES,QUEUE,waiting time distribution,renewal process},
  language     = {eng},
  number       = {4},
  pages        = {783--794},
  publisher    = {Applied Probability Trust},
  series       = {Journal of Applied Probability},
  title        = {Stationarity properties of neural networks},
  volume       = {35},
  year         = {1998},
}