Keywords
- Banach Space
- Covariance Operator
- Gaussian Measure
- Iterate Logarithm
- Strong Convergence Theorem
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References
DE ACOSTA, A.: Inequalities for B-valued random vectors with applications to the strong law of large numbers. Ann. Prob. 9 (1981), 157–161
DE ACOSTA, A. and KUELBS, J.: Some results on the cluster set C((Sn/an)) and the LIL. Ann. Prob. 11 (1983), 102–122
AZLAROV, T.A. and VOLODIN, N.A.: Laws of large numbers for identically distributed Banach space valued random variables. Theor. of Prob. Appl. 26 (1981), 573–580
BECK, A.: A convexity condition in Banach spaces and the strong law of large numbers. Proc. Amer. Math. Soc. 13 (1962), 329–334
CHEVET, S.: Gaussian measures and large deviations. Probability in Banach spaces 4, Oberwolfach 1982, Lecture Notes in Math 990, 30–46
CHOW, Y.S.: Local convergence of martingales and the law of large numbers. Ann. Math. Statist. 36 (1965), 552–558
FELLER, W.: A limit theorem for random variables with infinite moments. Amer. J. Math. 68 (1946), 257–262
FORTET, R. et MOURIER, E.: Les fonctions aléatoires comme éléments aléatoires dans les espaces de Banach. Stud. Math. 15 (1955), 62–79.
GOODMAN, V., KUELBS, J. and ZINN, J.: Some results on the law of the iterated logarithm in Banach space with applications to weighted empirical processes. Ann. Prob. 9 (1981), 713–752
HEINKEL, B.: On the law of large numbers in 2-uniformly smooth Banach spaces. (1983) to appear in Ann. Prob.
HEINKEL, B.: Une extension de la loi des grands nombres de Prohorov. preprint 1983
HOFFMANN-JØRGENSEN, J.: On the modulus of smoothness and the Gα-conditions in B-spaces. Aarhus Preprint Series 1974–75 no2
HOFFMANN-JØRGENSEN, J. and PISIER, G.: The law of large numbers and the the central-limit theorem in Banach spaces. Ann. Prob. 4 (1976), 587–599
KUELBS, J.: An inequality for the distribution of a sum of certain Banach space valued random variables. Stud. Math. 52 (1974), 69–87
KUELBS, J.: The law of the iterated logarithm and related strong convergence theorems for Banach space valued random variables. Ecole d’été de Probabilités de St-Flour 4 (1975)-Lecture Notes in Math 539, 225–314
KUELBS, J.: A strong convergence theorem for Banach space valued random variables. Ann. Prob. 4 (1976), 744–771
KUELBS, J.: The law of the iterated logarithm for Banach space valued random variables. Probability in Banach spaces 3, Medford 1980, Lecture Notes in Math 860, 268–278
KUELBS, J. and ZINN, J.: Some stability results for vector valued random variables. Ann. Prob. 7 (1979), 75–84
LEDOUX, M.: Sur les théorèmes limites dans certains espaces de Banach lisses. Probability in Banach spaces 4, Oberwolfach 1982, Lecture Notes in Math 990, 150–169
MAUREY, B. et PISIER, G.: Séries de variables aléatoires vectorielles indépendantes et propriétés géométriques des espaces de Banach. Stud. Math. 58 (1976), 45–90
MEYER, P.A.: Martingales and stochastic integrals I. Lecture Notes in Math 284 (1972)
MOURIER, E.: Les éléments aléatoires dans un espace de Banach. Ann. Inst. H. Poincaré 13 (1953), 159–244
PISIER, G.: Le théorème de la limite centrale et la loi du logarithme itéré dans les espaces de Banach. Séminaire Maurey-Schwartz 1975–76-Ecole Polytechnique-exposés no 3 et 4
PROHOROV, YU.V.: An extremal problem in probability theory. Theor. Prob. Appl. 4 (1959), 201–203
STOUT, W.F.: Almost sure convergence. Academic Press New York 1974
WOYCZYNSKI, W.A.: On the Marcinkiewicz-Zygmund laws of large numbers in Banach spaces and related rates of convergence. Prob. and Math. Stat. 1 (1980), 117–131
WOYCZYNSKI, W.A.: Survey of asymptotic behavior of sums of independent random vectors and general martingales in Banach spaces. Probability in Banach spaces 4, Oberwolfach 1982, Lecture Notes in Math 990, 215–220
YURINSKII, V.V.: Exponential bounds for large deviations. Theor. Prob. Appl. 19 (1974), 154–155
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© 1984 Springer-Verlag
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Heinkel, B. (1984). The non i.i.d. strong law of large numbers in 2-uniformly smooth Banach spaces. In: Szynal, D., Weron, A. (eds) Probability Theory on Vector Spaces III. Lecture Notes in Mathematics, vol 1080. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0099787
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DOI: https://doi.org/10.1007/BFb0099787
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