Stationarity properties of neural networks
(1998) In Journal of Applied Probability 35(4). p.783794 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 Nvector 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.
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/1273195
 author
 Asmussen, Sören ^{LU} and Turova, Tatyana ^{LU}
 organization
 publishing date
 1998
 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
 14756072
 language
 English
 LU publication?
 yes
 id
 fc375721454b4a7facd534241daaab94 (old id 1273195)
 date added to LUP
 20081209 14:04:00
 date last changed
 20180107 10:05:34
@article{fc375721454b4a7facd534241daaab94, 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 Nvector 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 = {14756072}, 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 = {783794}, publisher = {Applied Probability Trust}, series = {Journal of Applied Probability}, title = {Stationarity properties of neural networks}, volume = {35}, year = {1998}, }