Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-12-05T02:10:23.247Z Has data issue: false hasContentIssue false
  • English
  • Français

Expected number of excursions above curved boundarie by a random walk

Published online by Cambridge University Press:  17 April 2009

Fima C. Klebaner
Fima C. Klebaner
Affiliation:
Department of StatisticsThe University of MelbourneParkville Vic 3052Australia
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.

An asymptotic relation for the expected number of excursions above a boundary g(n) by a random walk Sn, n = 1,2, ‥, N is given in terms of an integral involving g. An integral test is given to determine whether the total excursion time has finite expectation. If some moment assumptions hold then the expectation of the total excursions is finite if and only if .

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 41 , Issue 2 , April 1990 , pp. 207 - 213
Copyright
Copyright © Australian Mathematical Society 1990

References

[1]Breiman, L., Probability (Addison-Wesley, Reading, 1968).Google Scholar
[2]Dieudonne, J., Infinitesimal Calculus (Hermann, Paris, 1971).Google Scholar
[3]Feller, W., An Introduction to Probability Theory and Its Applications 1 (John Wiley & Sons, New York, 1968).Google Scholar
[4]Feller, W., An Introduction to Probability Theory and Its Applications 2 (John Wiley & Sons, New York, 1971).Google Scholar
[5]Feller, W., ‘The general form of the so-called law of the iterated logarithm’, Trans. Amer. Math. Soc. 54 (1943), 373–402.CrossRefGoogle Scholar
[6]Petrov, V.V., Sums of Independent Random Variables (Springer, Berlin, Heidelberg, New York, 1975).Google Scholar