14-12-2025
جامعة الملك عبدالعزيز
KING ABDULAZIZ UNIVERSITY
Faculty of Sciences
Document Details
Document Type
:
Article In Journal
Document Title
:
Tightness of probability measures on function spaces
Tightness of probability measures on function spaces
Subject
:
Mthematics
Document Language
:
English
Abstract
:
Let CE = C ([0 1], E) be the Banach space, with the supremum norm, of all continuous functions f from the unit interval [0 1] into the Banach space E. If E = R we put CR = C. Function spaces under consideration are equipped with their Borel σ-field. This paper deals with the tightness property of some classes of probability measures (p.m) on the function space CE. We will be concerned mainly with the specific cases E = R, E = C and more generally E a separable Banach space. We give sufficient conditions for tightness by extending and strengthening the conditions developed by Prohorov in connection with limit theorems of stochastic processes. In the general case of a separable Banach space E, the property of tightness will be settled under conditions of different nature from those of Prohorov. Finally weak convergence of p.m on CE will be established under the condition of weak convergence of their finite dimensional distributions. This extends a similar result valid in the space C. © 2008 Elsevier Inc. All rights reserved.
ISSN
:
0022-247X
Journal Name
:
Journal of Mathematical Analysis and Applications
Volume
:
354
Issue Number
:
1
Publishing Year
:
2009 AH
2009 AD
Number Of Pages
:
4
Article Type
:
Article
Added Date
:
Tuesday, October 13, 2009
Researchers
Researcher Name (Arabic)
Researcher Name (English)
Researcher Type
Dr Grade
Email
لخضر مبارك بلعيد مزياني
مزياني
Researcher
Doctorate
mezianilakhdar@hotmail.com
Files
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Type
Description
23402.pdf
pdf
Abstract
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