Source: Ann. Inst. H. Poincaré Probab. Statist. Volume 46, Number 2
(2010), 575-593.
This is a continuation of the earlier work (Publ. Res. Inst. Math. Sci. 45 (2009) 745–785) to characterize unitary stationary independent increment Gaussian processes. The earlier assumption of uniform continuity is replaced by weak continuity and with technical assumptions on the domain of the generator, unitary equivalence of the process to the solution of an appropriate Hudson–Parthasarathy equation is proved.
Cet article poursuit la recherche initiée dans (Publ. Res. Inst. Math. Sci. 45 (2009) 745–785) pour caractériser les processus stationnaires unitaires gaussiens à incréments indépendants. L’hypothèse antérieure d’uniforme continuité est remplacée par de la continuité faible. Avec des conditions techniques sur le domaine du générateur, nous montrons que le processus est équivalent unitairement à la solution d’une équation de Hudson–Parthasarathy appropriée.
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