WHY IS KEMENY'S CONSTANT A CONSTANT?

被引：16

作者：

Bini, Dario ^{[1
]}

Hunter, Jeffrey J. ^{[2
]}

Latouche, Guy ^{[3
]}

Meini, Beatrice ^{[1
]}

Taylor, Peter ^{[4
]}

机构：

[1] Univ Pisa, Dipartimento Matemat, I-56127 Pisa, Italy

[2] Auckland Univ Technol, Dept Math Sci, Auckland 1142, New Zealand

[3] Univ Libre Bruxelles, Dept Informat, B-1050 Brussels, Belgium

[4] Univ Melbourne, Sch Math & Stat, Melbourne, Vic 3010, Australia

来源：

JOURNAL OF APPLIED PROBABILITY | 2018年 / 55卷 / 04期

基金：

澳大利亚研究理事会;

关键词：

Kemeny's constant; discrete-time Markov chain; continuous-time Markov chain; passage time; deviation matrix; STRONG ERGODICITY;

D O I：

10.1017/jpr.2018.68

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：

In their 1960 book on finite Markov chains, Kemeny and Snell established that a certain sum is invariant. The value of this sum has become known as Kemeny's constant. Various proofs have been given over time, some more technical than others. We give here a very simple physical justification, which extends without a hitch to continuous-time Markov chains on a finite state space. For Markov chains with denumerably infinite state space, the constant may be infinite and even if it is finite, there is no guarantee that the physical argument will hold. We show that the physical interpretation does go through for the special case of a birth-and-death process with a finite value of Kemeny's constant.

引用

页码：1025 / 1036

页数：12

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