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WROCŁAW UNIVERSITY
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TECHNOLOGY

Contents of PMS, Vol. 10, Fasc. 1,
pages 119 - 135
 

WEAK CONVERGENCE TO THE BROWNIAN MOTION OF THE PARTIAL SUMS OF INFIMA OF INDEPENDENT RANDOM VARIABLES

H. Hebda-Grabowska

Abstract: Let (Y ,n > 1) n be a sequence of independent, positive random variables, defined on a probability space (_O_,A, P), with the common distribution function F.

Put Y *= inf(Y ,Y ,...,Y ),m > 1, m 1 2 m and

sum n Sn = Ym*, n > 2,S1 = 0. m=1

The aim of this note is to give the rate of weak convergence of (Sn,n > 1) to the Brownian motion. Moreover, the mixing limit theorem and the random functional limit theorem for the sums Sn,n > 1, are presented.

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

Key words and phrases: -

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