Bernoulli

  • Bernoulli
  • Volume 21, Number 2 (2015), 647-696.

Spatio-temporal hybrid (PDMP) models: Central limit theorem and Langevin approximation for global fluctuations. Application to electrophysiology

Martin G. Riedler and Michèle Thieullen

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Abstract

In the present work we derive a central limit theorem for sequences of Hilbert-valued Piecewise Deterministic Markov process models and their global fluctuations around their deterministic limit identified by the law of large numbers. We provide a version of the limiting fluctuations processes in the form of a distribution valued stochastic partial differential equation which can be the starting point for further theoretical and numerical analysis. We also present applications of our results to two examples of hybrid models of spatially extended excitable membranes: compartmental-type neuron models and neural fields models. These models are fundamental in neuroscience modelling both for theory and numerics.

Article information

Source
Bernoulli, Volume 21, Number 2 (2015), 647-696.

Dates
First available in Project Euclid: 21 April 2015

Permanent link to this document
https://projecteuclid.org/euclid.bj/1429624957

Digital Object Identifier
doi:10.3150/13-BEJ583

Mathematical Reviews number (MathSciNet)
MR3338643

Zentralblatt MATH identifier
1327.60063

Keywords
central limit theorem global fluctuations infinite-dimensional stochastic processes Langevin approximation law of large numbers neural field models neuronal membrane models Piecewise Deterministic Markov Processes stochastic excitable media

Citation

Riedler, Martin G.; Thieullen, Michèle. Spatio-temporal hybrid (PDMP) models: Central limit theorem and Langevin approximation for global fluctuations. Application to electrophysiology. Bernoulli 21 (2015), no. 2, 647--696. doi:10.3150/13-BEJ583. https://projecteuclid.org/euclid.bj/1429624957


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