Moderate deviations of density-dependent Markov chains

被引：7

作者：

Xue, Xiaofeng ^{[1
]}

机构：

[1] Beijing Jiaotong Univ, Sch Sci, Beijing 100044, Peoples R China

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2021年 / 140卷

基金：

中国国家自然科学基金;

关键词：

Density-dependent Markov chain; Moderate deviation; Exponential martingale; PROBABILITIES; MARTINGALES;

D O I：

10.1016/j.spa.2021.06.005

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：

A density dependent Markov chain (DDMC) introduced in Kurtz (1978) is a special continuous time Markov process. Examples are considered in fields like epidemics and processes which describe chemical reactions. Moreover the Yule process is a further example. In this paper we prove a moderate deviation principle for the paths of a certain class of DDMC. The proofs of the bounds utilize an exponential martingale as well as a generalized version of Girsanov's theorem. The exponential martingale is defined according to the generator of the DDMC. (C) 2021 Elsevier B.V. All rights reserved.

引用

页码：49 / 80

页数：32

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