Geodesic
Atomic decompositions and inequalities for vector-valued discrete-time martingales
Teoriâ veroâtnostej i ee primeneniâ, Tome 43 (1998) no. 3, pp. 588-598

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider martingales with discrete time taking values in a Banach lattice $X$ that has UMD-property (UMD means unconditionality of martingale differences). We suppose that the UMD-lattice $X$ consists of real-valued functions. Two notions of maximal value for such martingales are introduced (in the case of real-valued martingales these notions are the same and also coincide with the notion of usual maximal value). We also introduce the notion of quadratic variation and both usual and predictable classes of martingale spaces corresponding to maximal values and quadratic variation. The equivalence of these classes is established. In particular, Davis inequalities are proved with the help of atomic decompositions. The case of a regular stochastic basis is considered separately.
Keywords: vector-valued martingales with discrete time, UMD-lattice, quadratic variation, Burkholder–Davis–Gundy inequalities, regular stochastic basis.
Mots-clés : maximal value, atomic decomposition 
@article{TVP_1998_43_3_a9,
     author = {F. Weisz and Yu. S. Mishura},
     title = {Atomic decompositions and inequalities for vector-valued discrete-time martingales},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {588--598},
     publisher = {mathdoc},
     volume = {43},
     number = {3},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1998_43_3_a9/}
}
TY  - JOUR
AU  - F. Weisz
AU  - Yu. S. Mishura
TI  - Atomic decompositions and inequalities for vector-valued discrete-time martingales
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 1998
SP  - 588
EP  - 598
VL  - 43
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TVP_1998_43_3_a9/
LA  - ru
ID  - TVP_1998_43_3_a9
ER  - 
%0 Journal Article
%A F. Weisz
%A Yu. S. Mishura
%T Atomic decompositions and inequalities for vector-valued discrete-time martingales
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1998
%P 588-598
%V 43
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TVP_1998_43_3_a9/
%G ru
%F TVP_1998_43_3_a9
F. Weisz; Yu. S. Mishura. Atomic decompositions and inequalities for vector-valued discrete-time martingales. Teoriâ veroâtnostej i ee primeneniâ, Tome 43 (1998) no. 3, pp. 588-598. http://geodesic.mathdoc.fr/item/TVP_1998_43_3_a9/