Belavkin, V. P. and Kolokoltsov, V. N. (Vasiliĭ Nikitich) (2002) Stochastic evolution as a quasiclassical limit of a boundary value problem for Schrödinger equations. Infinite Dimensional Analysis, Quantum Probability and Related Topics, Vol.5 (No.1). pp. 61-91. doi:10.1142/S0219025702000717 ISSN 0219 0257.

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Abstract

We develop systematically a new unifying approach to the analysis of
linear stochastic, quantum stochastic and even deterministic equations in
Banach spaces. Solutions to a wide class of these equations (in particular those decribing the processes of continuous quantum measurements)
are proved to coincide with the interaction representations of the solutions to certain Dirac type equations with boundary conditions in pseudo
Fock spaces. The latter are presented as the semi-classical limit of an appropriately dressed unitary evolutions corresponding to a boundary-value
problem for rather general Schrödinger equations with bounded below
Hamiltonians.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Statistics
Library of Congress Subject Headings (LCSH):	Stochastic processes, Banach spaces, Schrödinger equation
Journal or Publication Title:	Infinite Dimensional Analysis, Quantum Probability and Related Topics
Publisher:	World Scientific Publishing
ISSN:	0219 0257
Official Date:	2002
Dates:	Date Event 2002 Published
Volume:	Vol.5
Number:	No.1
Page Range:	pp. 61-91
DOI:	10.1142/S0219025702000717
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access

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