Positive Definite Germs of Quantum Stochastic Processes

Details Positive Definite Germs of Quantum Stochastic Processes Positive Definite Germs of Quantum Stochastic Processes

2005-12-13

arxiv.org/abs/math/0512289v1

C. R. Acad. Sc. Paris, 322 (1) 385--390 (1996)

Mathematics

Probability

8 pages, with French brief version

Scientific paper

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.

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