First passage time densities in non-Markovian models with subthreshold oscillations

Verechtchaguina, T., Sokolov, I. M., Schimansky-Geier, L. (2006) First passage time densities in non-Markovian models with subthreshold oscillations. Europhysics Letters, 73 (5). pp. 691-697. ISSN 0295-5075

URL: http://iopscience.iop.org/article/10.1209/epl/i200...
DOI: 10.1209/epl/i2005-10449-7

Abstract

Motivated by the dynamics of resonant neurons we consider a differentiable, non-Markovian random process x(t) and particularly the time after which it will reach a certain level x(b) for the first time. The probability density of this first passage time is expressed as infinite series of integrals over joint probability densities of x and its velocity (x) over dot. Approximating higher-order terms of this series through the lower-order ones leads to closed expressions in the cases of vanishing and moderate correlations between subsequent crossings of x(b). For a linear oscillator driven by white or coloured Gaussian noise, which models a resonant neuron, we show that these approximations reproduce the complex structures of the first passage time densities characteristic for the underdamped dynamics, where Markovian approximations ( giving monomodal first passage time distribution) fail.

Item Type: Paper
Uncontrolled Keywords: noise neurons threshold systems kramers
Subjects: organs, tissues, organelles, cell types and functions > tissues types and functions > neural networks
organs, tissues, organelles, cell types and functions > cell types and functions > cell types > neurons
organs, tissues, organelles, cell types and functions > cell types and functions > cell types > neurons
organs, tissues, organelles, cell types and functions > cell types and functions > cell types > neurons
CSHL Authors:
Communities: CSHL labs > Engel lab
Depositing User: Matt Covey
Date Deposited: 14 Aug 2017 18:24
Last Modified: 14 Aug 2017 18:24
URI: http://repository.cshl.edu/id/eprint/35099

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