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

## 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 |
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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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