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The eigentime identity for continuous-time ergodic Markov chains

Published online by Cambridge University Press:  14 July 2016

Yong-Hua Mao*
Affiliation:
Beijing Normal University
*
Postal address: Department of Mathematics, Beijing Normal University, Beijing 100875, P. R. China. Email address: [email protected]

Abstract

The eigentime identity is proved for continuous-time reversible Markov chains with Markov generator L. When the essential spectrum is empty, let {0 = λ0 < λ1 ≤ λ2 ≤ ···} be the whole spectrum of L in L2. Then ∑ n≥1 λ n -1 < ∞ implies the existence of the spectral gap α of L in L. Explicit formulae are presented in the case of birth–death processes and from these formulae it is proved that ∑ n≥1 λ n -1 < ∞ if and only if α > 0.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 2004 

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