Stochastic integrals of point processes and the decomposition of two- parameter martingales
type: Item
instance of: scholarly article
title: Stochastic integrals of point processes and the decomposition of two- parameter martingales
zbMATH Open document ID: 0682.60034
DOI: 10.1016/0047-259X(89)90090-0
author: P. Imkeller
published in: Journal of Multivariate Analysis
publication date: 1989-01-01T00:00:00Z
review text: Let M be a two-parameter square-integrable martingale with trajectories that have limits in all quadrants and are continuous from the right. The paper gives the decomposition of M into four orthogonal components: \(M=\sum^{4}_{i=1}M_ i,\) where \(M_ 1\) is continuous, \(M_ 2\) is purely discontinuous, \(M_ 3\) and \(M_ 4\) are continuous in one coordinate and purely discontinuous in the other coordinate. \(M_ 2\), \(M_ 3\) and \(M_ 4\) are represented as stochastic integrals with some point measures as integrators.
Mathematics Subject Classification ID: 60G44
Mathematics Subject Classification ID: 60G48
Mathematics Subject Classification ID: 60G57
Mathematics Subject Classification ID: 60H05
zbMATH DE Number: 4117565
zbMATH Keywords: two-parameter martingale
zbMATH Keywords: orthogonal decomposition
zbMATH Keywords: point measures as integrators
reviewed by: Yuliya S. Mishura
MaRDI profile type: Publication
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full work available at URL: 0047-259x(89)90090-0
OpenAlex ID: W2087089687
description: scientific article; zbMATH DE number 4117565