Abstract
Consider an irreducible time-homogeneous Markov chain with discrete time. The recurrence-time moments of the states of such stochastic processes are studied. We point out that if the recurrence time of one state has its first k moments finite, then the recurrence times of all the other states have their first k moments finite. We then specialize and investigate the recurrence-time moments of random walks. The main result of the paper consists of exhibiting random walks whose first k — 1 recurrence-time moments exist and whose higher moments are infinite, for k - 1, 2, …. A comparison theorem is derived that permits the moment properties of recurrence times of a large class of random walks to be determined.
Chapter PDF
Similar content being viewed by others
References
W. Feller, An introduction to probability theory and its applications, Wiley, New York, 1950.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Davis, R.A., Lii, KS., Politis, D.N. (2011). Recurrence-Time Moments in Random Walks. In: Davis, R., Lii, KS., Politis, D. (eds) Selected Works of Murray Rosenblatt. Selected Works in Probability and Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8339-8_10
Download citation
DOI: https://doi.org/10.1007/978-1-4419-8339-8_10
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-8338-1
Online ISBN: 978-1-4419-8339-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)