Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

Characterizations of processes with stationary and independent increments under $G$-expectation

Yongsheng Song

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Our purpose is to investigate properties for processes with stationary and independent increments under $G$-expectation. As applications, we prove the martingale characterization of $G$-Brownian motion and present a pathwise decomposition theorem for generalized $G$-Brownian motion.


Notre but est d’étudier des propriétés de processus à accroissements stationnaires et indépendants sous une $G$-espérance. Comme application, nous démontrons la caractérisation de la martingale de $G$-mouvement Brownien et fournissons un théorème de décomposition trajectorielle pour le $G$-mouvement Brownien généralisé.

Article information

Ann. Inst. H. Poincaré Probab. Statist., Volume 49, Number 1 (2013), 252-269.

First available in Project Euclid: 29 January 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G10: Stationary processes 60G17: Sample path properties 60G48: Generalizations of martingales 60G51: Processes with independent increments; Lévy processes

Stationary increments Independent increments Martingale characterization Decomposition theorem $G$-Brownian motion $G$-expectation


Song, Yongsheng. Characterizations of processes with stationary and independent increments under $G$-expectation. Ann. Inst. H. Poincaré Probab. Statist. 49 (2013), no. 1, 252--269. doi:10.1214/12-AIHP492.

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