- Full text PDF available (7)
We consider normal Markovian cocycles on a von Neu-mann algebra which are adapted to a Fock filtration. Every such cocycle k which is Markov-regular and consists of completely positive contractions is realised as a conditioned *-homomorphic cocycle. This amounts to a stochastic gener-alisation of a recent dilation result for norm-continuous normal… (More)
A new method for the construction of Fock-adapted operator Mar-kovian cocycles is outlined, and its use is illustrated by application to a number of examples arising in physics and probability. The construction uses the Trotter-Kato Theorem and a recent characterisation of such cocycles in terms of an associated family of contraction semigroups.
A Trotter product formula is established for unitary quantum stochastic processes governed by quantum stochastic differential equations with constant bounded coefficients.
Correspondence In their article " National Missile Defense and the Future of U.S. Nuclear Weapons Policy , " Charles Glaser and Steve Fetter perform a valuable service for readers of International Security and, more generally, the U.S. debate on national missile defense (NMD). 1 Their nonpolemical treatment of the technical, military, diplomatic, and… (More)
We develop fully noncommutative Feynman–Kac formulae by employing quantum stochastic processes. To this end we establish some theory for perturbing quantum stochastic flows on von Neumann algebras by multiplier cocycles. Multiplier cocycles are constructed via quantum stochastic differential equations whose coefficients are driven by the flow. The resulting… (More)
The theory of quantum Lévy processes on a compact quantum group, and more generally quantum stochastic convolution cocycles on a C *-bialgebra, is extended to locally compact quantum groups and multiplier C *-bialgebras. Strict extension results obtained by Kustermans, and automatic strictness properties developed here, are exploited to obtain existence and… (More)
Two new approaches to the infinitesimal characterisation of quantum stochastic cocycles are reviewed. The first concerns mapping cocycles on an operator space and demonstrates the role of Hölder continuity; the second concerns contraction operator cocycles on a Hilbert space and shows how holo-morphic assumptions yield cocycles enjoying an infinitesimal… (More)