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


VOLUMES
42.1 41.2 41.1 40.2 40.1 39.2 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. 9, Fasc. 1,
pages 95 - 114
 

TIGHTNESS CRITERIA FOR RANDOM MEASURES WITH APPLICATION TO THE PRINCIPLE OF CONDITIONING IN HILBERT SPACES

Adam Jakubowski

Abstract: Suppose that (m )
  n is a sequence of random probability measures on a real and separable Hilbert space such that, for each n  (-  N, m
 n  is a pointwisely convergent convolution of some sequence (m  | k  (-  N)
  nk of random measures. The sequence (m )
  n is said to be shift- tight if one can find random vectors (A )
  n such that the ”centered” sequence (m * d   )
  n  - An is tight.

It is proved that for a shift-tight sequence (m )
  n there exists a ”progressively measurable” centering which changes (m )
  n into a tight sequence.

As an application, Principle of Conditioning and Martingale Central Limit Theorem in a Hilbert space are proved.

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

Key words and phrases: -

Download:    Abstract    Full text   Abstract + References