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Positive Definite Germs of Quantum Stochastic Processes

Research paper by V. P. Belavkin

Indexed on: 13 Dec '05Published on: 13 Dec '05Published in: Mathematics - Probability



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.