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WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 12, Fasc. 1,
pages 113 - 125
 

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

Halina Hebda-Grabowska

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

  *                                n sum    *
Ym = inf(Y1,Y2,...,Ym), m > 1,  Sn =    Ym,n > 2,S1 = 0.
                                  m=1

In this paper a convergence rate in the invariance principle for the sums Sn, n > 1, is obtained.

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

Key words and phrases: -

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