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Limit theorems in fluctuation theory

Published online by Cambridge University Press:  01 July 2016

N. H. Bingham
N. H. Bingham*
Affiliation:
Westfield College, London
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Abstract

We shall be concerned here with limit theorems arising in the fluctuation theory of random walks, processes with stationary independent increments, recurrent events and regenerative phenomena. In Section 1 on discrete time, we consider limit theorems for ladder-points (Theorem 1) and for maxima of partial sums of random variables (Theorem 2), and discuss some related questions. In Section 2 (Theorems 3 to 6) we consider the analogues of these results in continuous time.

Keywords

SPITZER'S IDENTITYREGULAR VARIATIONTAUBERIAN THEOREMSLADDER POINTSRECURRENT EVENTSMAXIMA OF SUMS OF RANDOM VARIABLESp-FUNCTIONSSUPREMUM FUNCTIONALFIRST-PASSAGE FUNCTIONALREGENERATIVE PHENOMENA
Type
Research Article
Information
Advances in Applied Probability , Volume 5 , Issue 3 , December 1973 , pp. 554 - 569
Copyright
Copyright © Applied Probability Trust 1973 

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