各种稳定性统一的速度估计（英文）  

Unified Speed Estimation of Various Stabilities

作　　者：陈木法[1,2] 

机构地区：[1]北京师范大学数学科学学院 [2]北京师范大学数学与复杂系统教育部重点实验室,北京100875

出　　处：《应用概率统计》2016年第1期1-22,共22页Chinese Journal of Applied Probability and Statistics

基　　金：supported in part by the National Natural Science Foundation of China(No.11131003);the"985"project from the Ministry of Education in China;the Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions

摘　　要：为研究一些无穷维对象(例如统计物理中的相变),人们发展了若干数学工具,其一为各种稳定性/不稳定性的速度估计.本文对于最简单的一类马尔可夫过程一生灭过程的各种稳定性/不稳定性,汇集了一些预料不到的、统一的、近乎精确的基本估计.还讨论了若干背景和扩充.本文源于在几个国际会议上的报告.To study some infinite-dimensional subject （the phase transitions in statistical physics, for instance）, several mathematical tools are developed. One of them is the speed estimation of various stabilities/instabilities. This paper collects some unexpected, unified, nearly sharp basic estimates of various types of stability/instability for the simplest class of Markov processes, the birth-death processes. Some motivations and a part of extensions are also discussed. The paper is based on a talk presented recently in several international conferences.

关 键 词：稳定性 第一非平凡特征值 HARDY型不等式 杀死 速度估计 判准 生灭过程 

分 类 号：O211.62[理学—概率论与数理统计]