UNIVERSITY
OF WROCŁAW
 
Main Page
Contents
Online First
General Information
Instructions for authors


VOLUMES
43.1 42.2 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. 33, Fasc. 1,
pages 1 - 27
 

ON STRONG CONVERGENCE OF PRAMARTS IN BANACH SPACES

Mohammed Saadoune

Abstract: We present new versions of strong convergence results for Banach-space-valued pramarts based on various tightness conditions combined with uniform integrability conditions of Mazur type. They extend a result of Egghe [7] stating that every Banach-space-valued pramart with a Cesŕro-mean convergent subsequence converges strongly almost surely. Similar results are obtained for pramarts with values in the dual of a separable Banach space.

2000 AMS Mathematics Subject Classification: Primary: 60B11, 60B12, 60G48.

Keywords and phrases: Pramart, conditional expectation, tightness conditions, strong convergence, σ -measurable function, Lé vy’s theorem.

Download:    Abstract    Full text   Abstract + References