Quantum stochastic differential equations driven by free noises and dilations of Markovian semigroups
type: Item
instance of: scholarly article
title: Quantum stochastic differential equations driven by free noises and dilations of Markovian semigroups
zbMATH Open document ID: 0803.60053
author: Maria Elvira Mancino
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 1995-01-03T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/108316
review text: Quantum stochastic calculus with respect to free noises has been used to produce different dilations of Markovian semigroups with bounded generators. The aim of this paper is to extend these results to a bigger class of Markovian semigroups. For this end we establish an existence, uniqueness and unitary theorem for quantum stochastic differential equations with unbounded coefficients driven by infinite creation and annihilation and gauge fields. We show that, even if the free noise fields satisfy a different Itô table, it turns out that the unitary cocycles obtained as solutions of quantum stochastic differential equations driven by free noise fields, can be used to construct unitary dilations of the same class of quantum stochastic differential equations dilated by unitary cocycles in the boson Fock space.
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 81S25
Mathematics Subject Classification ID: 60K40
zbMATH DE Number: 627430
zbMATH Keywords: quantum stochastic calculus
zbMATH Keywords: Markovian semigroups
zbMATH Keywords: quantum stochastic differential equations
zbMATH Keywords: creation
zbMATH Keywords: annihilation
zbMATH Keywords: gauge fields
zbMATH Keywords: unitary cocycles
zbMATH Keywords: free noise fields
zbMATH Keywords: unitary dilations
zbMATH Keywords: boson Fock space
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 627430