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

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 mast...

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Bibliographic Details
Published in:Nagoya mathematical journal 1996-03, Vol.141, p.29-43
Main Authors: Barchielli, A., Paganoni, A. M.
Format: Article
Language:English
Subjects:
60B99
60H99
81S25
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Summary: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.
ISSN:0027-7630
2152-6842
DOI:10.1017/S0027763000005511