Quantum stochastic differential equations in terms of quantum white noise

敏彦 有光

Toshihico Arimitsu

Dong Myung Chung, Un Cig Ji, Nobuaki Obata

White noise theory allows to formulate quantum white noises explicitly as elemental quantum stochastic processes. A traditional quantum stochastic differential equation of Itô type is brought into a normal-ordered white noise differential equation driven by lower powers of quantum white noises. The class of normal-ordered white noise differential equations covers quantum stochastic differential equations with highly singular noises such as higher powers or higher order derivatives of quantum white noises, which are far beyond the traditional Itô theory. For a general normal-ordered white noise differential equation unique existence of a solution is proved in the sense of white noise distribution. Its regularity properties are investigated by means of weighted Fock spaces interpolating spaces of white noise distributions and associated characterization theorems for S-transform and for operator symbols.

J. Martin Lindsay, Adam Skalski

Luigi Accardi, Andreas Boukas

We prove the stochastic independence of the basic integrators of the renormalized square of white noise (SWN). We use this result to deduce the unitarity conditions for stochastic differential equations driven by the SWN.

V. P. Belavkin, Jaeseong Heo, Un Cig Ji