On regularity of multiparameter amarts and martingales. (English) Zbl 0438.60042


60G48 Generalizations of martingales
60G42 Martingales with discrete parameter
60G40 Stopping times; optimal stopping problems; gambling theory
Full Text: DOI


[1] Astbury, K., Amarts indexed by directed sets, Ann. Probab., 6, 267-278 (1978) · Zbl 0378.60017
[2] Bakry, D., Sur la régularité des trajectoires des martingales à deux indices, Z. Wahrscheinlichkeitstheorie verw. Gebiete, 50, 149-157 (1979) · Zbl 0419.60051
[3] Bakry, D.: Sur la théorie des processus à deux indices, Exposé III: Limites “quadrantales” des martingales. Université de Strasbourg, Séminaire de Probabilité. [To appear)
[4] Brennan, M. D., Planar Semimartingales, J. Multivariate Analy., 9, 465-486 (1979) · Zbl 0456.60049
[5] Cairoli, R., Une inégalité pour martingales à indices multiples, Lecture Notes in Math. 124, 1-27 (1970), Berlin-Heidelberg-New York: Springer, Berlin-Heidelberg-New York · Zbl 0218.60045
[6] Cairoli, R.; Walsh, J. B., Stochastic integrals in the plane, Acta Math., 134, 111-183 (1975) · Zbl 0334.60026
[7] Dellacherie, C.; Meyer, P. A., Probabilities and Potential (1978), Amsterdam: North-Holland, Amsterdam
[8] Doob, J. L., Stochastic Processes (1953), New York: Wiley, New York · Zbl 0053.26802
[9] Edgar, G. A.; Sucheston, L., Amarts: A class of asymptotic martingales, A: Discrete parameter, B: Continuous parameter, J. Multivariate Anal., 5, 193-221 (1976) · Zbl 0336.60033
[10] Gabriel, J. P., An inequality for sums of independent random variables indexed by finitedimensional filtering sets, and its applications to the convergence of series, Ann. Probab., 5, 779-786 (1977) · Zbl 0376.60057
[11] Jessen, B.; Marcinkiewicz, J.; Zygmund, A., Note on differentiability of multiple integrals, Fund. Math., 25, 217-234 (1935) · JFM 61.0255.01
[12] Millet, A.; Sucheston, L., Classes d’amarts filtrants et conditions de Vitali, C.R. Acad. Sci. Paris, Série A, 286, 835-837 (1977) · Zbl 0384.60031
[13] Millet, A.; Sucheston, L., Convergence of classes of amarts indexed by directed sets, Canadian J. Math., 32, 86-125 (1980) · Zbl 0448.60036
[14] Millet, A.; Sucheston, L., A characterization of Vitali conditions in terms of maximal inequalities, Ann. Probab., 8, 339-349 (1980) · Zbl 0428.60053
[15] Millet, A., Sucheston, L.: On convergence of L1-bounded martingales indexed by directed sets. Probability and Mathematical Statistics [To appear) · Zbl 0502.60033
[16] Millet, A.; Sucheston, L., On covering conditions and convergence, Lecture Notes in Math. Vol. 794, 431-454 (1980), Berlin Heidelberg New York: Springer, Berlin Heidelberg New York
[17] Millet, A.; Sucheston, L., Convergence et régularité des martingales à indices multiples, C.R. Acad. Sci. Paris, Série A, 291, 147-150 (1980) · Zbl 0445.60031
[18] Neveu, J.: Mathematical foundations of the calculus of probability. Holden-Day 1965 · Zbl 0137.11301
[19] Neveu, J., Discrete parameter martingales (1975), Amsterdam: North Holland, Amsterdam · Zbl 0345.60026
[20] Walsh, J. B., Convergence and regularity of multiparameter strong martingales, Z. Wahrscheinlichkeitstheorie verw. Gebiete, 46, 177-192 (1979) · Zbl 0395.60040
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