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A note on a formula of the Lévy-Khinchin type in quantum probability

Published online by Cambridge University Press:  22 January 2016

A. Barchielli  and
A. M. Paganoni
A. Barchielli
Affiliation:
Università di Milano, Dipartimento di Matematica, Via Saldini 50, I-20133 Milano, Italy and Istituto Nationale di Fisica Nucleare Istituto Nationale di Fisica Nucleare
A. M. Paganoni
Affiliation:
Università di Milano, Dipartimento di Matematica, Via Saldini 50, I-20133 Milano, Italy and Istituto Nationale di Fisica Nucleare Istituto Nationale di Fisica Nucleare
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In the past few years there has been an increasing interest in a certain class of stochastic differential equations (SDE’s) in Hilbert spaces for applications in quantum mechanics (measurements continuous in time [1-5]) and in quantum optics (photon-detection theory and numerical simulations of master equations [6-10]). Part of the mathematical theory of these equations has been developed in [11], where also “structural properties” of this class of equations have been studied. In the paper [11] it has been shown that such equations are connected with certain semigroups of linear operators and the form of the generator of semigroups related to such SDE’s has been established.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 141 , March 1996 , pp. 29 - 43
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1996

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