Stopping unitary processes in Fock space
type: Item
instance of: scholarly article
title: Stopping unitary processes in Fock space
zbMATH Open document ID: 0659.60096
author: David Applebaum
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 1988-01-01T00:00:00Z
review text: Let \(P^ T\) be a stop time in symmetric Fock space over \(L^ 2({\mathbb{R}}^+)\). We show that to certain unitary operator valued processes \(U=(U(t),t\geq 0)\) which satisfy a stochastic differential equation driven by ``non-commutative noise'' in Fock space tensored with an ``initial'' Hilbert space, we can associate a stopped operator U(t). We use these operators to prove a ``stopped cocycle relation'' whereby for \(P^ T\) finite the process \((U(T+t)\), \(t\geq 0)\) is factorized as the product of U(T) with a new process \(U^ T=(U^ T(t)\), \(t\geq 0)\) beginning ``after time T''.
Mathematics Subject Classification ID: 60H99
Mathematics Subject Classification ID: 60H10
zbMATH DE Number: 4078428
zbMATH Keywords: stop time in symmetric Fock space
zbMATH Keywords: unitary operator valued processes
zbMATH Keywords: stochastic differential equation
zbMATH Keywords: non-commutative noise
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195174688
OpenAlex ID: W2021749068
cites work: The strong Markov property for canonical Wiener processes
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cites work: Q3740712
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DOI: 10.2977/PRIMS/1195174688
description: scientific article; zbMATH DE number 4078428