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On the law of the iterated logarithm for inter-record times

Published online by Cambridge University Press:  14 July 2016

William E. Strawderman  and
Paul T. Holmes
William E. Strawderman
Affiliation:
Rutgers University
Paul T. Holmes
Affiliation:
Rutgers University
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Extract

Let X1, X2, X3, ··· be independent, identically distributed random variables on a probability space (Ω, F, P); and with a continuous distribution function. Let the sequence of indices {Vr} be defined as Also define The following theorem is due to Renyi [5].

Type
Research Papers
Information
Journal of Applied Probability , Volume 7 , Issue 2 , August 1970 , pp. 432 - 439
Copyright
Copyright © Applied Probability Trust 1970 

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References

[1] Chung, K. L. (1968) A Course in Probability Theory. Harcourt Brace and World, Inc., New York.Google Scholar
[2] Feller, W. (1966) An Introduction to Probability Theory and Its Applications, Vol. II. Wiley, New York.Google Scholar
[3] Holmes, P. T. and Strawderman, W. (1969) A note on the waiting times between record observations. J. Appl. Prob. 6, 711–714.Google Scholar
[4] Neuts, M. F. (1967) Waiting times between record observations. J. Appl. Prob. 4, 206–208.Google Scholar
[5] Rényi, A. (1962) Théorie des éléments saillants d'une suite d'observations. Colloquium on Combinatorial Methods in Probability Theory. Mathematisk Institut, Aarhus Universitet, Denmark, 104–115.Google Scholar
[6] Tata, M. N. (1969) On outstanding values in a sequence of random variables. Z. Wahrscheinlichkeitsth. 12, 9–20.Google Scholar