Predictability and stopping on lattices of sets
type: Item
instance of: scholarly article
title: Predictability and stopping on lattices of sets
zbMATH Open document ID: 0794.60025
DOI: 10.1007/BF01192958
author: B. Gail Ivanoff
author: Ely Merzbach
author: Ioana Schiopu Kratina
publication date: 1994-08-28T00:00:00Z
review text: As a first step in the development of a general theory of set-indexed martingales, we define predictability on a general space with respect to a filtration indexed by a lattice of sets. We prove a characterization of the predictable \(\sigma\)-algebra in terms of adapted and ``left- continuous'' processes without any form of topology for the index set. We then define a stopping set and show that it is a natural generalization of the stopping time; in particular, the predictable \(\sigma\)-algebra can be characterized by various stochastic intervals generated by stopping sets.
Mathematics Subject Classification ID: 60G07
Mathematics Subject Classification ID: 60G60
zbMATH DE Number: 568997
zbMATH Keywords: set-indexed martingales
zbMATH Keywords: filtration indexed by a lattice of sets
zbMATH Keywords: stopping time
zbMATH Keywords: stochastic intervals
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01192958
OpenAlex ID: W1985169537
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 568997