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

被引：12

作者：

Pakdaman, Khashayar ^{[2
]}

Thieullen, Michele ^{[3
]}

Wainrib, Gilles ^{[1
]}

机构：

[1] Univ Paris 13, Lab Anal Geometrie & Applicat, Inst Gallilee, F-93410 Villetaneuse, France

[2] Univ Paris 07, Inst Jacques Monod, UMR7592, F-75205 Paris 13, France

[3] Univ Paris 06, Lab Probabil & Modeles Aleatoires, UMR7599, F-75252 Paris 05, France

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2012年 / 122卷 / 06期

关键词：

Piecewise-deterministic Markov process; Averaging; Homogenization; Central limit theorem; Multiscale; Slow-fast; Neuron models with stochastic ion channels; BEHAVIOR; NOISE; MODEL;

D O I：

10.1016/j.spa.2012.03.005

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We consider a general class of piecewise-deterministic Markov processes with multiple time-scales. In line with recent results on the stochastic averaging principle for these processes, we obtain a description of their law through an asymptotic expansion. We further study the fluctuations around the averaged system in the form of a central limit theorem, and derive consequences on the law of the first passage-time. We apply the mathematical results to the Morris-Lecar model with stochastic ion channels. (C) 2012 Elsevier B.V. All rights reserved.

引用

页码：2292 / 2318

页数：27

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