Verechtchaguina, T., Sokolov, I. M., Schimansky-Geier, L. (March 2006) First passage time densities in non-Markovian models with subthreshold oscillations. Europhysics Letters, 73 (5). pp. 691-697. ISSN 0295-5075
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: | March 2006 |
| Date Deposited: | 14 Aug 2017 18:24 |
| Last Modified: | 14 Aug 2017 18:24 |
| URI: | https://repository.cshl.edu/id/eprint/35099 |
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