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A compactness principle for bounded sequences of martingales with applications

Delbaen, Freddy and Schachermayer, Walter (1999) A compactness principle for bounded sequences of martingales with applications. Report Series SFB "Adaptive Information Systems and Modelling in Economics and Management Science", 23. SFB Adaptive Information Systems and Modelling in Economics and Management Science, WU Vienna University of Economics and Business, Vienna.

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Abstract

For H^1 bounded sequences, we introduce a technique, related to the Kadec-Pelczynski -decomposition for L^1 sequences, that allows us to prove compactness theorems. Roughly speaking, a bounded sequence in H^1 can be split into two sequences, one of which is weakly compact, the other forms the singular part. If the martingales are continuous then the singular part tends to zero in the semi-martingale topology. In the general case the singular parts give rise to a process of bounded variation. The technique allows to give a new proof of the optional decomposition theorem in Mathematical Finance. (author's abstract)

Item Type: Paper
Divisions: Departments > Informationsverarbeitung u Prozessmanag. > Produktionsmanagement > Taudes
Departments > Finance, Accounting and Statistics > Statistics and Mathematics
Departments > Marketing > Service Marketing und Tourismus
Departments > Informationsverarbeitung u Prozessmanag. > Informationswirtschaft
Depositing User: Repository Administrator
Date Deposited: 08 Mar 2002 09:03
Last Modified: 14 Sep 2010 16:58
URI: http://epub.wu.ac.at/id/eprint/1604

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