Stationarity properties of neural networks

Sören Asmussen, Tatyana Turova

Research output: Contribution to journalArticlepeer-review

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.
Original languageEnglish
Pages (from-to)783-794
JournalJournal of Applied Probability
Volume35
Issue number4
Publication statusPublished - 1998

Subject classification (UKÄ)

  • Probability Theory and Statistics

Free keywords

  • inhibition
  • ladder height distribution
  • Palm theory
  • path decomposition
  • queuing theory
  • random walk
  • MARTINGALES
  • QUEUE
  • waiting time distribution
  • renewal process

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