Positive Definite Germs of Quantum Stochastic Processes
نویسنده
چکیده
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 Itô 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. Germes positivement definis de processus quantiques stochastiques Résumé. On trouve une characterisation des différentielles stochastiques des processus quantiques positifs définis (PD) pour une algèbre de Itô arbitraire. On démontre un théorème de représentation qui donne la dilatation pseudoHilbertienne de la matrice des germes de la différentielle. Ceci suggère une forme générale des équations d’évolution quantiques stochastiques par rapport aux sauts de Poisson, à la diffusion de Wiener ou aux bruits quantiques généralisés. Version française abrégée.
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