Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

Characterization of unitary processes with independent and stationary increments

Lingaraj Sahu and Kalyan B. Sinha

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Abstract

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.

Résumé

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.

Article information

Source
Ann. Inst. H. Poincaré Probab. Statist. Volume 46, Number 2 (2010), 575-593.

Dates
First available in Project Euclid: 11 May 2010

Permanent link to this document
http://projecteuclid.org/euclid.aihp/1273584135

Digital Object Identifier
doi:10.1214/09-AIHP327

Zentralblatt MATH identifier
05758861

Mathematical Reviews number (MathSciNet)
MR2667710

Subjects
Primary: 60G51: Processes with independent increments; Lévy processes 81S25: Quantum stochastic calculus

Keywords
Unitary processes Noise space Hudson–Parthasarathy equations

Citation

Sahu, Lingaraj; Sinha, Kalyan B. Characterization of unitary processes with independent and stationary increments. Ann. Inst. H. Poincaré Probab. Statist. 46 (2010), no. 2, 575--593. doi:10.1214/09-AIHP327. http://projecteuclid.org/euclid.aihp/1273584135.


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