63 citations · 195 across the 10 of their papers we have counts for
9 papers · 2 filters
Quantum Stochastic Differential Equation
V. P. Belavkin, P. Staszewski
A semi-classical non-Hamiltonian model of a spontaneous collapse of unstable quantum system is given. The time evolution of the system becomes non-Hamiltonian at random instants of…
A Quantum Nonadapted Ito Formula and Stochastic Analysis in Fock scale
V. P. Belavkin
A generalized definition of quantum stochastic (QS) integrals and differentials is given in the free of adaptiveness and basis form in terms of Malliavin derivative on a projective…
On Stochastic Schroedinger Equation as a Dirac Boundary-value Problem, and an Inductive Stochastic Limit
V. P. Belavkin
We prove that a single-jump quantum stochastic unitary evolution is equivalent to a Dirac boundary value problem on the half line in one extra dimension. It is shown that this exac…
On Quantum Ito Algebras and their decompositions
V. P. Belavkin
A simple axiomatic characterization of the noncommutative Ito algebra is given and a pseudo-Euclidean fundamental representation for such algebra is described. It is proved that ev…
Quantum Continual Measurements and a Posteriori Collapse on CCR
V. P. Belavkin
A quantum theory for the Markovian dynamics of an open system under the unsharp observation which is continuous in time, is developed within the CCR stochastic approach. A stochast…
A Dynamical Theory of Quantum Measurement and Spontaneous Localization
V. P. Belavkin
We develop a rigorous treatment of discontinuous stochastic unitary evolution for a system of quantum particles that interacts singularly with quantum "bubbles" at random instants…