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Escape rates in periodically driven Markov processes

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  • Schindler, Michael
  • Talkner, Peter
  • Hänggi, Peter

Abstract

We present an approximate analytical expression for escape rates 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.

Suggested Citation

  • Schindler, Michael & Talkner, Peter & Hänggi, Peter, 2005. "Escape rates in periodically driven Markov processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 351(1), pages 40-50.
    • Handle: RePEc:eee:phsmap:v:351:y:2005:i:1:p:40-50
    DOI: 10.1016/j.physa.2004.12.020
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    References listed on IDEAS

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    1. Ebeling, Werner & Molgedey, Lutz & Reimann, Axel, 2000. "Stochastic urn models of innovation and search dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 599-612.
    2. Antonio Di Crescenzo & Luigi M. Ricciardi, 2001. "On a discrimination problem for a class of stochastic processes with ordered first‐passage times," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 17(2), pages 205-219, April.
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    Cited by:

    1. Molini, A. & Talkner, P. & Katul, G.G. & Porporato, A., 2011. "First passage time statistics of Brownian motion with purely time dependent drift and diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(11), pages 1841-1852.
    2. Aniello Buonocore & Luigia Caputo & Enrica Pirozzi & Luigi M. Ricciardi, 2011. "The First Passage Time Problem for Gauss-Diffusion Processes: Algorithmic Approaches and Applications to LIF Neuronal Model," Methodology and Computing in Applied Probability, Springer, vol. 13(1), pages 29-57, March.
    3. Duan, Wei-Long & Fang, Hui & Zeng, Chunhua, 2019. "The stability analysis of tumor-immune responses to chemotherapy system with gaussian white noises," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 96-102.
    4. Buonocore, A. & Caputo, L. & Nobile, A.G. & Pirozzi, E., 2014. "Gauss–Markov processes in the presence of a reflecting boundary and applications in neuronal models," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 799-809.
    5. Meier, Christian & Li, Lingfei & Zhang, Gongqiu, 2023. "Simulation of multidimensional diffusions with sticky boundaries via Markov chain approximation," European Journal of Operational Research, Elsevier, vol. 305(3), pages 1292-1308.

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