Our purpose is to investigate properties for processes with stationary and independent increments under -expectation. As applications, we prove the martingale characterization of -Brownian motion and present a pathwise decomposition theorem for generalized -Brownian motion.
Notre but est d’étudier des propriétés de processus à accroissements stationnaires et indépendants sous une -espérance. Comme application, nous démontrons la caractérisation de la martingale de -mouvement Brownien et fournissons un théorème de décomposition trajectorielle pour le -mouvement Brownien généralisé.
Keywords: stationary increments, independent increments, martingale characterization, decomposition theorem, $G$-Brownian motion, $G$-expectation
@article{AIHPB_2013__49_1_252_0, author = {Song, Yongsheng}, title = {Characterizations of processes with stationary and independent increments under $G$-expectation}, journal = {Annales de l'I.H.P. Probabilit\'es et statistiques}, pages = {252--269}, publisher = {Gauthier-Villars}, volume = {49}, number = {1}, year = {2013}, doi = {10.1214/12-AIHP492}, mrnumber = {3060156}, zbl = {1282.60050}, language = {en}, url = {http://archive.numdam.org/articles/10.1214/12-AIHP492/} }
TY - JOUR AU - Song, Yongsheng TI - Characterizations of processes with stationary and independent increments under $G$-expectation JO - Annales de l'I.H.P. Probabilités et statistiques PY - 2013 SP - 252 EP - 269 VL - 49 IS - 1 PB - Gauthier-Villars UR - http://archive.numdam.org/articles/10.1214/12-AIHP492/ DO - 10.1214/12-AIHP492 LA - en ID - AIHPB_2013__49_1_252_0 ER -
%0 Journal Article %A Song, Yongsheng %T Characterizations of processes with stationary and independent increments under $G$-expectation %J Annales de l'I.H.P. Probabilités et statistiques %D 2013 %P 252-269 %V 49 %N 1 %I Gauthier-Villars %U http://archive.numdam.org/articles/10.1214/12-AIHP492/ %R 10.1214/12-AIHP492 %G en %F AIHPB_2013__49_1_252_0
Song, Yongsheng. Characterizations of processes with stationary and independent increments under $G$-expectation. Annales de l'I.H.P. Probabilités et statistiques, Volume 49 (2013) no. 1, pp. 252-269. doi : 10.1214/12-AIHP492. http://archive.numdam.org/articles/10.1214/12-AIHP492/
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