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On the maximum and absorption time of left-continuous random walk

Published online by Cambridge University Press:  14 July 2016

Anthony G. Pakes
Anthony G. Pakes*
Affiliation:
Princeton University
*
∗On leave from the Department of Mathematics, Monash University, Clayton, Victoria, Australia.
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Abstract

In a recent paper Green (1976) obtained some conditional limit theorems for the absorption time of left-continuous random walk. His methods require that in the driftless case the increment distribution has exponentially decreasing tails and that the same is true for a transformed distribution in the case of negative drift.

Here we take a different approach which will produce Green's results under minimal conditions. Limit theorems are given for the maximum as the initial position of the random walk tends to infinity.

Keywords

LEFT-CONTINUOUS RANDOM WALKMAXIMUMABSORPTION TIMELIMIT THEOREMSLOCAL LIMIT THEOREMSRENEWAL THEOREMS
Type
Research Papers
Information
Journal of Applied Probability , Volume 15 , Issue 2 , June 1978 , pp. 292 - 299
Copyright
Copyright © Applied Probability Trust 1978 

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Footnotes

Research sponsored in part by a contract with the Office of Naval Research, No. N00014–75–C–0453, awarded to the Department of Statistics, Princeton University.

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