Positive Definite Germs of Quantum Stochastic Processes
Probability
2007-05-23 v1
Abstract
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.
Cite
@article{arxiv.math/0512289,
title = {Positive Definite Germs of Quantum Stochastic Processes},
author = {V. P. Belavkin},
journal= {arXiv preprint arXiv:math/0512289},
year = {2007}
}
Comments
8 pages, with French brief version