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.
| Author: | Michael SchindlerGND, Peter TalknerGND, Peter HänggiORCiDGND |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-2788 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/344 |
| Type: | Preprint |
| Language: | English |
| 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: www.elsevier.com/locate/physa |
| 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 |
