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Stationarity properties of neural networks

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Søren Asmussen  and
Tatyana S. Turova
Søren Asmussen*
Affiliation:
University of Lund
Tatyana S. Turova*
Affiliation:
University of Lund
*
∗Postal address: Department of Mathematical Statistics, University of Lund, Box 118, 221 00 Lund, Sweden
∗Postal address: Department of Mathematical Statistics, University of Lund, Box 118, 221 00 Lund, Sweden
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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 θ(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 θ(i) and Y(i) do not depend upon i. The tools are probabilistic and involve path decompositions, Palm theory and random walks.

Keywords

Inhibitionladder height distributionpath decompositionPalm theoryrandom walkqueuing theoryrenewal processwaiting time distribution

MSC classification

Primary: 60K10: Applications (reliability, demand theory, etc.)
Secondary: 60K05: Renewal theory 60K20: Applications of Markov renewal processes (reliability, queueing networks, etc.) 60K25: Queueing theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 35 , Issue 4 , December 1998 , pp. 783 - 794
Copyright
Copyright © Applied Probability Trust 1998 

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Footnotes

TT was partially supported by Astra Draco.

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