Regularity and decomposition of two-parameter supermartingales
type: Item
instance of: scholarly article
title: Regularity and decomposition of two-parameter supermartingales
zbMATH Open document ID: 0574.60058
DOI: 10.1016/0047-259X(85)90093-4
published in: Journal of Multivariate Analysis
publication date: 1985-01-01T00:00:00Z
review text: In the first section of this article the Doob-Meyer decomposition of a supermartingale is extended in several ways to two-parameter stochastic processes. In particular the notion of Laplacian is introduced which gives a more explicit decomposition for potentials. The second section is devoted to the optional sampling theorem and to several possible notions of two-parameter local martingales. In the final section the authors give sufficient conditions for a two-parameter process to have right- continuous trajectories with limits in all the quadrants. Moreover the authors find a relation between regularity of certain quasimartingales and continuity of the associated integrable variation process.
reviewed by: M.Dozzi
Mathematics Subject Classification ID: 60G60
Mathematics Subject Classification ID: 60G44
zbMATH DE Number: 3917379
zbMATH Keywords: Doob-Meyer decomposition
zbMATH Keywords: two-parameter stochastic processes
zbMATH Keywords: decomposition for potentials
zbMATH Keywords: optional sampling theorem
zbMATH Keywords: two-parameter local martingales
author: Gerald Mazziotto
author: Ely Merzbach
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3917379