Positive Definite Germs of Quantum Stochastic Processes
Abstract
Description
A new notion of stochastic germs for quantum processes is introduced and a characterisation of the stochastic differentials for positive definite (PD) processes is found in terms of their germs for arbitrary Ito algebra. A representation theorem, giving the pseudo-Hilbert dilation for the germ-matrix of the differential, is proved. This suggests the general form of quantum stochastic evolution equations with respect to the Poisson (jumps), Wiener (diffusion) or general quantum noise.
8 pages, with French brief version
8 pages, with French brief version