Stationarity properties of neural networks
(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.
Please use this url to cite or link to this publication:
https://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
- 1475-6072
- language
- English
- LU publication?
- yes
- id
- fc375721-454b-4a7f-acd5-34241daaab94 (old id 1273195)
- date added to LUP
- 2016-04-04 08:43:01
- date last changed
- 2022-01-29 03:53:42
@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}}, keywords = {{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}}, }