Abstract:
:This article presents a new theoretical framework to consider the dynamics of a stochastic spiking neuron model with general membrane response to input spike. We assume that the input spikes obey an inhomogeneous Poisson process. The stochastic process of the membrane potential then becomes a gaussian process. When a general type of the membrane response is assumed, the stochastic process becomes a Markov-gaussian process. We present a calculation method for the membrane potential density and the firing probability density. Our new formulation is the extension of the existing formulation based on diffusion approximation. Although the single Markov assumption of the diffusion approximation simplifies the stochastic process analysis, the calculation is inaccurate when the stochastic process involves a multiple Markov property. We find that the variation of the shape of the membrane response, which has often been ignored in existing stochastic process studies, significantly affects the firing probability. Our approach can consider the reset effect, which has been difficult to deal with by analysis based on the first passage time density.
journal_name
Neural Computjournal_title
Neural computationauthors
Amemori KI,Ishii Sdoi
10.1162/089976601317098529subject
Has Abstractpub_date
2001-12-01 00:00:00pages
2763-97issue
12eissn
0899-7667issn
1530-888Xjournal_volume
13pub_type
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