Doob-Meyer decomposition of Hilbert space valued functions
type: Item
instance of: scholarly article
title: Doob-Meyer decomposition of Hilbert space valued functions
zbMATH Open document ID: 1038.60036
published in: Journal of Theoretical Probability
publication date: 2004-03-15T00:00:00Z
review text: (1) This paper gives a new proof of the Doob-Meyer decomposition which is rather quick and elementary. It is more general in some aspects, and weaker in other aspects if compared to other approaches. The functions are defined on a totally ordered set with image in a Hilbert space. (2) This paper also gives a second variant of the Doob-Meyer decomposition; it is more specialized. (3) This paper applies (1) by reproving the Doléans measure in a special setting and demonstrates that the stochastic integral could be defined on more general totally ordered time scales than \(\mathbb{R}\).
reviewed by: Yuhu Feng
Mathematics Subject Classification ID: 60G44
Mathematics Subject Classification ID: 60B11
Mathematics Subject Classification ID: 60H05
zbMATH DE Number: 2057320
zbMATH Keywords: Doob-Meyer decomposition
zbMATH Keywords: Hilbert space
zbMATH Keywords: totally ordered set
zbMATH Keywords: Doléans measure
zbMATH Keywords: stochastic integral
author: Bernhard Burgstaller
MaRDI profile type: Publication
full work available at URL: b:jotp.0000011998.44302.3b
OpenAlex ID: W2081239434
DOI: 10.1023/B:JOTP.0000011998.44302.3B
description: scientific article; zbMATH DE number 2057320