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The stochastic geyser problem for first-passage times

Published online by Cambridge University Press:  14 July 2016

Josef Steinebach
Josef Steinebach*
Affiliation:
University of Marburg
*
∗Postal address: Fachbereich Mathematik, Universität Marburg, Lahnberge, 3550 Marburg, W. Germany.
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Abstract

Let X1, X2, · ·· be a sequence of independent, identically distributed (i.i.d.) random variables with positive mean. An analogue of Rényi's (1962) stochastic geyser problem is solved for the associated process of first-passage times. More precisely, it is shown that a single realization of the sequence determines the distribution function (d.f.) of the Xn's almost surely (a.s.), even if the observations are erroneous up to an order o(log n).

Keywords

STOCHASTIC GEYSER PROBLEMFIRST-PASSAGE TIMESERDÖS–RÉNYI STRONG LAWERDÖS–RENYI INCREMENTS
Type
Research Papers
Information
Journal of Applied Probability , Volume 18 , Issue 1 , March 1981 , pp. 91 - 103
Copyright
Copyright © Applied Probability Trust 

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References

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