UNIVERSITY
OF WROCŁAW
 
Main Page
Contents of previous volumes
Forthcoming papers
General Information
Instructions for authors


VOLUMES
39.1 38.2 38.1 37.2 37.1 36.2 36.1
35.2 35.1 34.2 34.1 33.2 33.1 32.2
32.1 31.2 31.1 30.2 30.1 29.2 29.1
28.2 28.1 27.2 27.1 26.2 26.1 25.2
25.1 24.2 24.1 23.2 23.1 22.2 22.1
21.2 21.1 20.2 20.1 19.2 19.1 18.2
18.1 17.2 17.1 16.2 16.1 15 14.2
14.1 13.2 13.1 12.2 12.1 11.2 11.1
10.2 10.1 9.2 9.1 8 7.2 7.1
6.2 6.1 5.2 5.1 4.2 4.1 3.2
3.1 2.2 2.1 1.2 1.1
 
 
WROCŁAW UNIVERSITY
OF SCIENCE AND
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: -

Download:    Abstract    Full text   Abstract + References