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.
出处
《应用概率统计》
CSCD
北大核心
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
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
stability
the first （non-trivial） eigenvalue
Hardy-type inequality
killing
speed estimation
criterion
birth-death process
