Document Zbl 0516.60053

Demiconvergence of processes indexed by two indices. (English) Zbl 0516.60053

Ann. Inst. Henri Poincaré, Nouv. Sér., Sect. B 19, 175-187 (1983).

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MSC:

60G42	Martingales with discrete parameter
60G44	Martingales with continuous parameter
60G48	Generalizations of martingales
60G17	Sample path properties

Keywords:

processes indexed by two indices; demiconvergence; amart

Citations:

Zbl 0477.60051

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Full Text: Numdam EuDML

References:

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[2]	D. Bakry , Sur la régularité des trajectoires des martingales à deux indices. Z. Wahrscheinlichkeitstheorie verw. Geb. , t. 50 , 1979 , p. 149 - 157 . MR 551608 \| Zbl 0419.60051 · Zbl 0419.60051 · doi:10.1007/BF00533636
[3]	R. Cairoli , Une inégalité pour martingales à indices multiples . Séminaire de Probabilité IV . Université de Strasbourg . Lecture Notes in Math. , t. 124 , p. 1 - 27 . Berlin , Heidelberg , New York . Springer , 1970 . Numdam \| MR 270424 \| Zbl 0218.60045 · Zbl 0218.60045
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[5]	G.A. Edgar and L. Sucheston , Démonstrations de lois des grands nombres par les sous-martingales descendantes . C. R. Acad. Sci. Paris , t. 292 , Série I, 1981 , p. 967 - 969 . MR 631108 \| Zbl 0471.60035 · Zbl 0471.60035
[6]	H. Heinich , Convergence de sous-martingales positives dans un Banach réticulé , C. R. Acad. Sci. Paris , t. 286 , 1978 , p. 279 - 280 . MR 486301 \| Zbl 0383.60046 · Zbl 0383.60046
[7]	A. Millet and L. Sucheston , Convergence of classes of amarts indexed by directed sets , Canadian J. Math. , t. 32 , 1980 , p. 86 - 125 . MR 559789 \| Zbl 0448.60036 · Zbl 0448.60036 · doi:10.4153/CJM-1980-009-1
[8]	A. Millet and L. Sucheston , A characterization of Vitali Conditions in terms of maximal inequalities , Ann. Prob. , t. 8 , 1980 , p. 339 - 349 . Article \| MR 566598 \| Zbl 0428.60053 · Zbl 0428.60053 · doi:10.1214/aop/1176994781
[9]	A. Millet and L. Sucheston , On regularity of multiparameter amarts and martingales , Z. Wahrscheinlichkeitstheorie verw. Geb. , t. 56 , 1981 , p. 21 - 45 . MR 612158 \| Zbl 0438.60042 · Zbl 0438.60042 · doi:10.1007/BF00531972
[10]	P.A. Meyer , Théorie élémentaire des processus à deux indices . Lecture Notes Math. , t. 863 , 1981 , p. 1 - 39 . Springer-Verlag . MR 630303 \| Zbl 0461.60072 · Zbl 0461.60072
[11]	J. Neveu , Discrete parameter martingales . Amsterdam , North Holland , 1975 . MR 402915 \| Zbl 0345.60026 · Zbl 0345.60026
[12]	H.H. Schaefer , Banach lattices and positive operators , Springer-Verlag , Berlin , 1975 . MR 423039 \| Zbl 0296.47023 · Zbl 0296.47023
[13]	R.T. Smythe , Strong laws of large numbers for r-dimensional arrays of random variables , Ann. Prob. , t. 1 , 1973 , p. 164 - 170 . Article \| MR 346881 \| Zbl 0258.60026 · Zbl 0258.60026 · doi:10.1214/aop/1176997031

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