Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-22T05:34:29.869Z Has data issue: false hasContentIssue false
  • English
  • Français

On record values and record times

Published online by Cambridge University Press:  14 July 2016

R. W. Shorrock
R. W. Shorrock*
Affiliation:
The University of British Columbia
Get access Rights & Permissions [Opens in a new window]

Abstract

A correspondence between record values and independent increment point processes is established. The asymptotic behaviour of record value sequences is studied, and results on the asymptotic behaviour of record times (for continuous F) are obtained as special cases. The joint law of the kth record value and the kth record time is also derived.

Keywords

RECORD VALUERECORD TIMEPOINT PROCESSINDEPENDENT INCREMENT
Type
Research Papers
Information
Journal of Applied Probability , Volume 9 , Issue 2 , June 1972 , pp. 316 - 326
Copyright
Copyright © Applied Probability Trust 1972 

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

[1] Billingsley, P. (1968) Convergence of Probability Measures. John Wiley and Sons, New York.Google Scholar
[2] Breiman, L. (1968) Probability. Addison-Wesley, Reading, Mass.Google Scholar
[3] Feller, W. (1966) An Introduction to Probability Theory and its Applications. Volume II. John Wiley and Sons, New York.Google Scholar
[4] Jordon, C. (1965) Calculus of Finite Differences. Chelsea Publishing Company, New York.Google Scholar
[5] Rényi, A. (1962) Théorie des éléments saillants d'une suite d'observations. Colloq. Combinatorial Meth. Prob. Theory, Aarhus University, 104–115.Google Scholar
[6] Shorrock, R. W. (1972) A limit theorem for inter-record times. J. Appl. Prob. 9, 219–223.CrossRefGoogle Scholar
[7] Strawderman, W. and Holmes, P. T. (1970) On the law of the iterated logarithm for inter-record times. J. Appl. Prob. 7, 432–439.CrossRefGoogle Scholar
[8] Tata, M. N. (1969) On outstanding values in a sequence of random variables. Z. Wahrscheinlichkeitsth. 12, 9–20.Google Scholar