Escape rates in periodically driven Markov processes

  • We present an approximate analytical expression for the escape rate of time-dependent driven stochastic processes with an absorbing boundary such as the driven leaky integrate-and-fire model for neural spiking. The novel approximation is based on a discrete state Markovian modeling of the full long-time dynamics with time-dependent rates. It is valid in a wide parameter regime beyond the restraining limits of weak driving (linear response) and/or weak noise. The scheme is carefully tested and yields excellent agreement with three different numerical methods based on the Langevin equation, the Fokker-Planck equation and an integral equation.

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Author:Michael SchindlerGND, Peter TalknerGND, Peter HänggiGND
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Publishing Institution:Universität Augsburg
Release Date:2006/09/04
Tag:absorbing boundary; non-stationary Markov processes; Ornstein-Uhlenbeck process; rate process; periodic driving; driven neuron models
GND-Keyword:Markov-Prozess; Ornstein-Uhlenbeck-Prozess; Absorption
Source:erschienen in: Physica A 351, 40–50 (2005); doi:10.1016/j.physa.2004.12.020; URL:
Institutes:Mathematisch-Naturwissenschaftlich-Technische Fakultät
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Physik
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Physik / Lehrstuhl für Theoretische Physik I
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik