Characterization of unitary processes with independent and stationary increments
Annales de l'I.H.P. Probabilités et statistiques, Tome 46 (2010) no. 2, pp. 575-593.

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.

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.

DOI : 10.1214/09-AIHP327
Classification : 60G51, 81S25
Mots-clés : unitary processes, noise space, Hudson-Parthasarathy equations 
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Sahu, Lingaraj; Sinha, Kalyan B. Characterization of unitary processes with independent and stationary increments. Annales de l'I.H.P. Probabilités et statistiques, Tome 46 (2010) no. 2, pp. 575-593. doi : 10.1214/09-AIHP327. http://archive.numdam.org/articles/10.1214/09-AIHP327/

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