Quantum stochastic integrals under standing hypotheses
type: Item
instance of: scholarly article
title: Quantum stochastic integrals under standing hypotheses
zbMATH Open document ID: 0623.60066
DOI: 10.1016/0022-247X(87)90150-8
author: Raymond F. Streater
author: Christopher Barnett
author: Ivan F. Wilde
published in: Journal of Mathematical Analysis and Applications
publication date: 1987-01-01T00:00:00Z
review text: We study the meaning of stochastic integrals when the integrator is a quantum stochastic process which is not quite a martingale, in that it obeys estimates of the type advocated by \textit{E. J. McShane} [Stochastic calculus and stochastic models. (1974; Zbl 0292.60090)] in the classical case. We define the integral and solve stochastic differential equations when the von Neumann algebra is finite and when it has a cyclic and separating state or weight. When conditional expectations exist, a quantum martingale continuity theorem is proved.
Mathematics Subject Classification ID: 60H05
Mathematics Subject Classification ID: 81P20
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 46L51
Mathematics Subject Classification ID: 46L53
Mathematics Subject Classification ID: 46L54
zbMATH DE Number: 4011576
zbMATH Keywords: quantum stochastic process
zbMATH Keywords: von Neumann algebra
zbMATH Keywords: quantum martingale continuity theorem
MaRDI profile type: Publication
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full work available at URL: 0022-247x(87)90150-8
OpenAlex ID: W2072401938
description: scientific article; zbMATH DE number 4011576