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WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 6, Fasc. 2,
pages 217 - 223
 

RANDOM WALKS WITH RANDOM INDICES AND NEGATIVE DRIFT CONDITIONED TO STAY POSITIVE

A. Szubarga
D. Szynal

Abstract: Let (X ,k > 1)
  k be a sequence of independent, identically distributed random variables with E|X |= m < 0,
   1 and let (N ,n > 0),
  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 S   = X  + ...+X   ,
 Nn    1        Nn n > 1.

The main result in this paper shows (under appropriate conditions on (N ,n > 0)
  n and (X  ,k > 1)
   k ) that S
  Nn  conditioned on [S > 0,...,S   > 0]
  1        Nn converges weakly to a random variable S* considered by Iglehart [4].

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

Key words and phrases: -

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