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WROCŁAW UNIVERSITY
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TECHNOLOGY

Contents of PMS, Vol. 5, Fasc. 1,
pages 83 - 89
 

RANDOM LIMIT THEOREMS FOR RANDOM WALKS CONDITIONED TO STAY POSITIVE

A. Szubarga
D. Szynal

Abstract: Let (X ,k > 1) k be a sequence of independent, identically distributed random variables with EX = 0, 1 EX2 = s2 < oo , 1 and let (N ,n > 1), n N = 0 0 a.s., be a sequence of positive integer-valued random variables. Form the random walk (S ,n > 0) Nn by setting S = 0 0 and S = X + ...+ X , Nn 1 Nn n > 1. This paper investigates the limit behaviour of

P[S < xs V~ N-|S > 0,S > 0,...,S > 0]. Nn n 1 2 Nn

2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

Key words and phrases: -

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