Geodesic
On further classes of martingale-like sequences and some decomposition and convergence theorems
Glasgow mathematical journal, Tome 41 (1999) no. 3, pp. 313-322

Voir la notice de l'article provenant de la source Cambridge University Press

It is known that the class of mils generalizes that of pramarts and martingales in the limit. Also every Banach space-valued mil (Xn) with lim infnE(‖Xn‖)<∞ can be written in a unique form: $X_n=M_n+P_n(n\in\rm{N})$, where $(M_n)$ is a uniformly integrable martingale and $(P_n)$ converges to zero a.s. in norm. We shall show that this result still holds for a class which essentially generalizes that of mils. Another class of Banach space-valued martingale-like sequences, still containing all pramarts is defined and shown to have the decomposition above under the following much weaker condition: $\rm{lim inf}_{r\inT}E(\VertX_{\tau}\Vert)<\infty$, where T denotes the set of all bounded stopping times.1991 Mathematics Subject Classification. 60G48, 60B11. 
Luu, Dinh Quang. On further classes of martingale-like sequences and some decomposition and convergence theorems. Glasgow mathematical journal, Tome 41 (1999) no. 3, pp. 313-322. doi: 10.1017/S0017089599000245
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