Stochastic Dynamics of Spike Trains of Neuron Models for Firing Times with Exponential Decay and Jump-Diffusion

Herein we derive the first passage time density (FPTD) for a spike discharge in a single neuron with inputs that produce either inhibitory or excitatory impulses. We study the stochastic dynamics using imbedding approach and derive an integro-differential equation for the FPTD. By taking the kernel...

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Bibliographic Details
Published in:Journal of the Indian Society for Probability and Statistics 2017-12, Vol.18 (2), p.147-158
Main Authors: Vittal, P. R., Thangaraj, V., Venkateswaran, M.
Format: Article
Language:English
Subjects:
Mathematics and Statistics
Operations Research/Decision Theory
Probability Theory and Stochastic Processes
Research Article
Statistical Theory and Methods
Statistics
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Summary:Herein we derive the first passage time density (FPTD) for a spike discharge in a single neuron with inputs that produce either inhibitory or excitatory impulses. We study the stochastic dynamics using imbedding approach and derive an integro-differential equation for the FPTD. By taking the kernel in the master equation in separable form, we obtain a third order differential equation. Applying a suitable limiting procedure, we convert the differential equation into that of an O.U. process. Finally we introduce jump-diffusion to study the FPTD of spike train of a single neuron.
ISSN:2364-9569
2364-9569
DOI:10.1007/s41096-017-0023-y