Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-12T19:41:12.980Z Has data issue: false hasContentIssue false
  • English
  • Français

Persistent random walks may have arbitrarily large tails

Published online by Cambridge University Press:  01 July 2016

D. R. Grey
D. R. Grey*
Affiliation:
University of Sheffield
*
∗Postal address: Department of Probability and Statistics, The University, Sheffield S3 7RH, UK.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We give a probabilistic proof of a result of Shepp, that a symmetric random walk may have jump size distribution with arbitrarily large tails and yet still be persistent.

Keywords

PERSISTENCETRANSIENCETAIL BEHAVIOUR
Type
Letters to the Editor
Information
Advances in Applied Probability , Volume 21 , Issue 1 , March 1989 , pp. 229 - 230
Copyright
Copyright © Applied Probability Trust 1989 

References

Chung, K. L. and Fuchs, W. H. J. (1951) On the distribution of values of sums of random variables. Mem. Amer. Math. Soc. No. 6.CrossRefGoogle Scholar
Chung, K. L. and Ornstein, D. (1962) On the recurrence of sums of random variables. Bull. Amer. Math. Soc. 68, 30–32.CrossRefGoogle Scholar
Grey, D. R. (1978) Three lemmas after Besicovitch and their applications in probability theory. J. London Math. Soc. (2) 18, 173–180.Google Scholar
Grey, D. R. (1989) A note on explosiveness of Markov branching processes. Adv. Appl. Prob. 21, 226–228.CrossRefGoogle Scholar
Pitman, E. J. G. (1968) On the behaviour of the characteristic function of a probability distribution in the neighbourhood of the origin. J. Austral. Math. Soc. 8, 423–443.CrossRefGoogle Scholar
Shepp, L. A. (1964) Recurrent random walks with arbitrarily large steps. Bull. Amer. Math. Soc. 70, 540–542.Google Scholar
Spitzer, F. (1964) Principles of Random Walk. Van Nostrand, Princeton, N.J. Google Scholar
Stoyanov, J. M. (1987) Counterexamples in Probability. Wiley, Chichester.Google Scholar