STOCHASTIC EVOLUTION AS A QUASICLASSICAL LIMIT OF A BOUNDARY VALUE PROBLEM FOR SCHRÖDINGER EQUATIONS
2002 ◽
Vol 05
(01)
◽
pp. 61-91
Keyword(s):
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 describing 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 semiclassical limit of an appropriately dressed unitary evolutions corresponding to a boundary-value problem for rather general Schrödinger equations with bounded below Hamiltonians.
2019 ◽
Vol 266
(2-3)
◽
pp. 1121-1152
◽
2001 ◽
Vol 173
(1)
◽
pp. 79-91
◽
1996 ◽
Vol 21
(5-6)
◽
pp. 687-692
2013 ◽
Vol 33
(9)
◽
pp. 3861-3884
◽
2021 ◽
Vol 2
(6)
◽