Abstract
Let Nn denote the number of positive sums in the first n trials in a random walk (Si) and let Ln denote the first time we obtain the maximum in S0,..., Sn. Then the classical equivalence principle states that Nn and Ln have the same distribution and the classical arcsine law gives necessary and sufficient condition for (1/n) Ln or (1/n) Nn 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 (Tn) and to provide a simple an elementary proof of the equivalence principle for a general class of integer valued random vectors (Nn, Ln).
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