Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-23T15:58:03.531Z Has data issue: false hasContentIssue false
  • English
  • Français

On exponential ergodicity and spectral structure for birth-death processes

Published online by Cambridge University Press:  01 July 2016

Herman Callaert  and
Julian Keilson
Herman Callaert
Affiliation:
University of Louvain
Julian Keilson
Affiliation:
University of Rochester
Get access Rights & Permissions [Opens in a new window]

Abstract

An abstract is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.
Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Second conference on stochastic processes and applications
Information
Advances in Applied Probability , Volume 5 , Issue 1 , April 1973 , pp. 9 - 11
Copyright
Copyright © Applied Probability Trust 1973 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Callaert, H. (1971) Exponential Ergodicity for Birth-and-death Processes. , Leuven.Google Scholar
Feller, W. (1959) The birth-and-death processes as diffusion processes. J. Math. Pures Appl. 38, 301–345.Google Scholar
Karlin, S. and McGregor, J. L. (1957a) The differential equations of birth-and-death processes, and the Stieltjes moment problem. Trans. Amer. Math. Soc. 85, 489–546.CrossRefGoogle Scholar
Karlin, S. and McGregor, J. L. (1957b) The classification of birth-and-death processes. Trans. Amer. Math. Soc. 86, 366–400.Google Scholar
Keilson, J. (1965) A review of transient behavior in regular diffusion and birth-death processes. Part II. J. Appl. Prob. 2, 405–428.Google Scholar
Keilson, J. (1971) Log-concavity and log-convexity in passage time densities of diffusion and birth-death processes. J. Appl Prob. 8, 391–398.Google Scholar
Kendall, D. G. (1959a) Unitary dilations of Markov transition operators and the corresponding integral representations for transition-probability matrices. In Probability and Statistics. Ed. Grenander, U.. Almqvist and Wiksell, Stockholm.Google Scholar
Kingman, J. F. C. (1963a) The exponential decay of Markov transition probabilities. Proc. Lond. Math. Soc. (3) 13, 337–358.Google Scholar
Kingman, J. F. C. (1963b) Ergodic properties of continuous-time Markov processes and their discrete skeletons. Proc. Lond. Math. Soc. (3) 13, 593–604.Google Scholar