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BIRTH–DEATH CHAINS AND THE LOCAL TIME OF BROWNIAN MOTION

Part of: Markov processes

Published online by Cambridge University Press:  08 December 2011

GREG MARKOWSKY
GREG MARKOWSKY*
Affiliation:
Department of Mathematical Sciences, Monash University, Victoria, 3800, Australia (email: [email protected])
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Abstract

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A connection between Brownian motion and birth–death chains is explored. Several results concerning birth–death chains are shown to be consequences of well-known results on Brownian motion.

Keywords

birth–death chainMarkov chainBrownian motionlocal time

MSC classification

Secondary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 85 , Issue 3 , June 2012 , pp. 497 - 504
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

References

[1]Ahlfors, L. V., Complex Analysis: An Introduction to the Theory of Analytic Functions of One Complex Variable (McGraw-Hill, New York, 1966).Google Scholar
[2]Kallenberg, O., Foundations of Modern Probability (Springer, New York, 2002).CrossRefGoogle Scholar
[3]Klebaner, F. C., Introduction to Stochastic Calculus with Applications (Imperial College Press, London, 2005).Google Scholar
[4]Marcus, M. B. and Rosen, J., Markov Processes, Gaussian Processes and Local Times (Cambridge University Press, Cambridge, 2006).CrossRefGoogle Scholar
[5]Markowsky, G., ‘Applying Brownian motion to the study of birth–death chains’, Statist. Probab. Lett. 81(8) (2011), 1173–1178.CrossRefGoogle Scholar
[6]Revuz, D. and Yor, M., Continuous Martingales and Brownian Motion (Springer, Berlin, 1999).CrossRefGoogle Scholar