Characterizations of processes with stationary and independent increments under G-expectation
Annales de l'I.H.P. Probabilités et statistiques, Tome 49 (2013) no. 1, pp. 252-269.

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.

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.

DOI : 10.1214/12-AIHP492
Classification : 60G10, 60G17, 60G48, 60G51
Mots-clés : stationary increments, independent increments, martingale characterization, decomposition theorem, $G$-Brownian motion, $G$-expectation 
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Song, Yongsheng. Characterizations of processes with stationary and independent increments under $G$-expectation. Annales de l'I.H.P. Probabilités et statistiques, Tome 49 (2013) no. 1, pp. 252-269. doi : 10.1214/12-AIHP492. http://www.numdam.org/articles/10.1214/12-AIHP492/

[1] L. Denis, M. Hu and S. Peng. Function spaces and capacity related to a sublinear expectation: Application to G-Brownian motion pathes. Potential Anal. 34 (2011) 139-161. | MR | Zbl

[2] M. Hu and S. Peng. On representation theorem of G-expectations and paths of G-Brownian motion. Acta Math. Appl. Sin. Engl. Ser. 25 (2009) 539-546. | MR | Zbl

[3] S. Peng. G-expectation, G-Brownian motion and related stochastic calculus of Itô type. In Stochastic Analysis and Applications 541-567. Abel Symp. 2. Springer, Berlin, 2007. | MR | Zbl

[4] S. Peng. G-Brownian motion and dynamic risk measure under volatility uncertainty. Available at arXiv:0711.2834v1 [math.PR], 2007. | MR

[5] S. Peng. Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation. Stochastic Process. Appl. 118 (2008) 2223-2253. | MR | Zbl

[6] S. Peng. A new central limit theorem under sublinear expectations. Available at arXiv:0803.2656v1 [math.PR], 2008.

[7] S. Peng. Survey on normal distributions, central limit theorem, Brownian motion and the related stochastic calculus under sublinear expectations. Sci. China Ser. A 52 (2009) 1391-1411. | MR | Zbl

[8] S. Peng. Nonlinear expectations and stochastic calculus under uncertainty. Available at arXiv:1002.4546v1 [math.PR], 2010. | MR

[9] M. Soner, N. Touzi and J. Zhang. Martingale representation theorem under G-expectation. Stochastic Process. Appl. 121 (2011) 265-287. | MR | Zbl

[10] Y. Song. Some properties on G-evaluation and its applications to G-martingale decomposition. Sci. China Math. 54 (2011) 287-300. | MR | Zbl

[11] Y. Song. Properties of hitting times for G-martingales and their applications. Stochastic Process. Appl. 121 (2011) 1770-1784. | MR | Zbl

[12] Y. Song. Uniqueness of the representation for G-martingales with finite variation. Electron. J. Probab. 17 (2012) 1-15. | MR | Zbl

[13] J. Xu and B. Zhang. Martingale characterization of G-Brownian motion. Stochastic Process. Appl. 119 (2009) 232-248. | MR | Zbl

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