Asymptotic expansion and central limit theorem for multiscale piecewise-deterministic Markov processes

DOI10.1016/j.spa.2012.03.005zbMath1261.60031OpenAlexW1988362958MaRDI QIDQ429283

Khashayar Pakdaman, Michèle Thieullen, Gilles Wainrib

Publication date: 19 June 2012

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.spa.2012.03.005

zbMATH Keywords

homogenizationaveragingmultiscaleslow-fastneuron models with stochastic channelspiecewise-deterministic Markov processes

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Processes in random environments (60K37)

Related Items (10)

Averaging for a Fully Coupled Piecewise-Deterministic Markov Process in Infinite Dimensions ⋮ Moment bounds and geometric ergodicity of diffusions with random switching and unbounded transition rates ⋮ Averaging for slow–fast piecewise deterministic Markov processes with an attractive boundary ⋮ Stochastic hybrid systems in cellular neuroscience ⋮ Stochastic representations of ion channel kinetics and exact stochastic simulation of neuronal dynamics ⋮ Reduction of a stochastic model of gene expression: Lagrangian dynamics gives access to basins of attraction as cell types and metastabilty ⋮ Averaging principle and normal deviations for multiscale stochastic systems ⋮ Stability in Distribution of Path-Dependent Hybrid Diffusion ⋮ Exponential ergodicity for Markov processes with random switching ⋮ Spatio-temporal hybrid (PDMP) models: central limit theorem and Langevin approximation for global fluctuations. Application to electrophysiology

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