On stochastic differential equations and semigroups of probability operators in quantum probability

A. Barchielli, A. M. Paganoni and F. Zucca

Stochastic Processes and their Applications, 1998, vol. 73, issue 1, 69-86

Abstract: Some "classical" stochastic differential equations have been used in the theory of measurements continuous in time in quantum mechanics and, more generally, in quantum open system theory. In this paper, we introduce and study a class of such equations which allow us to achieve the same level of generality as the one obtained by the approach to continuous measurements based on semigroups of operators. To this aim, we have to study some linear and non-linear stochastic differential equations for processes in Hilbert spaces and in some related Banach spaces. By this stochastic approach we can also obtain new results on the evolution systems which substitute the semigroups of probability operators in the time inhomogeneous case.

Keywords: 60H10; 58D25; 47D06; 81P15 (search for similar items in EconPapers)
Date: 1998
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304-4149(97)00093-8
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:73:y:1998:i:1:p:69-86

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().