Journal article

ON STATIONARY DISTRIBUTIONS OF STOCHASTIC NEURAL NETWORKS

K Borovkov, G Decrouez, M Gilson

JOURNAL OF APPLIED PROBABILITY | CAMBRIDGE UNIV PRESS | Published : 2014

Abstract

The paper deals with nonlinear Poisson neuron network models with bounded memory dynamics, which can include both Hebbian learning mechanisms and refractory periods. The state of the network is described by the times elapsed since its neurons fired within the post-synaptic transfer kernel memory span, and the current strengths of synaptic connections, the state spaces of our models being hierarchies of finitedimensional components. We prove the ergodicity of the stochastic processes describing the behaviour of the networks, establish the existence of continuously differentiable stationary distribution densities (with respect to the Lebesgue measures of corresponding dimensionality) on the co..

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Grants

Awarded by ARC


Funding Acknowledgements

This research was supported by the ARC Discovery Grant DP120102398 and the ARC Centre of Excellence for Mathematics and Statistics of Complex Systems. The authors are grateful to the anonymous referee for useful comments that helped to improve the exposition of the paper.