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. 3, Fasc. 1,
pages 97 - 101
 

ON THE ALMOST SURE CONVERGENCE OF THE SQUARE VARIATION OF THE BROWNIAN MOTION

Andrzej Wróbel

Abstract: The paper deals with the problem of almost sure (a.s.) convergence of the square variation of the Brownian motion when the diameters d
 n  of partitions of the time interval tend to zero. It is known that if the diameters converge fast enough, namely if d
 n  is of order less than lg-1n , then a.s. convergence takes place. On the other hand, we show that there exists a sequence of partitions with diameters d
 n  of order less than lg-an for any 0 < a < 1 such that the Brownian square variation diverges a.s.

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

Key words and phrases: -

Download:    Abstract    Full text   Abstract + References