NDLI: The Arcsine Law

Content Provider	Springer Nature Link
Author	Hoffmann Jørgensen, J.
Copyright Year	1999
Abstract	Let N $_{n}$ denote the number of positive sums in the first n trials in a random walk (S $_{i}$) and let L $_{n}$ denote the first time we obtain the maximum in S $_{0}$,..., S $_{n}$. Then the classical equivalence principle states that N $_{n}$ and L $_{n}$ have the same distribution and the classical arcsine law gives necessary and sufficient condition for (1/n) L $_{n}$ or (1/n) N $_{n}$ to converge in law to the arcsine distribution. The objective of this note is to provide a simple and elementary proof of the arcsine law for a general class of integer valued random variables (T $_{n}$) and to provide a simple an elementary proof of the equivalence principle for a general class of integer valued random vectors (N $_{n}$, L $_{n}$).
Starting Page	131
Ending Page	145
Page Count	15
File Format	PDF
ISSN	08949840
Journal	Journal of Theoretical Probability
Volume Number	12
Issue Number	1
e-ISSN	15729230
Language	English
Publisher	Kluwer Academic Publishers-Plenum Publishers
Publisher Date	1999-01-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Probability Theory and Stochastic Processes Statistics
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Statistics, Probability and Uncertainty

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The Arcsine Law