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 language | English |
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Pages (from-to) | 783-794 |
Journal | Journal of Applied Probability |
Volume | 35 |
Issue number | 4 |
Publication status | Published - 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