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The exponential rate of convergence of the distribution of the maximum of a random walk. Part II

Published online by Cambridge University Press:  14 July 2016

N. Veraverbeke  and
J. L. Teugels
N. Veraverbeke
Affiliation:
Limburgs Universitair Centrum
J. L. Teugels
Affiliation:
Limburgs Universitair Centrum
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Abstract

Let Gn (x) be the distribution of the nth successive maximum of a random walk on the real line. Under conditions typical for complete exponential convergence, the decay of Gn (x) – limn→∞ Gn(x) is asymptotically equal to H(x) γn n–3/2 as n → ∞where γ < 1 and H(x) a function solely depending on x. For the case of drift to + ∞, G∞(x) = 0 and the result is new; for drift to – ∞we give a new proof, simplifying and correcting an earlier version in [9].

Keywords

COMPLETE EXPONENTIAL CONVERGENCEMAXIMUM (SUPREMUM) OF A RANDOM WALKEXPONENTIAL RATE OF CONVERGENCEEXPANSIONS FOR THE CENTRAL LIMIT THEOREM
Type
Research Papers
Information
Journal of Applied Probability , Volume 13 , Issue 4 , December 1976 , pp. 733 - 740
Copyright
Copyright © Applied Probability Trust 1976 

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References

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