Relations between laws of large numbers and asymptotic martingales in Banach spaces

 Access to full text

 Full (PDF)

1. [1] A. de Acosta, Inequalities for B-valued random vectors with applications to the strong law of large numbers, Ann. Probability9(1981), p.157-161. Zbl0449.60002MR606806
2. [2] P. Assouad, Espaces p-lisses et q-convexes. Inegalites de Burkholder, Seminaire Maurcy-Schwartz (1975), exp XV. Zbl0318.46023MR407963
3. [3] T.A. Azlarov and N.A. Volodin, The law of large numbers for identically distributed Banach space valued random variables, Teorya Veroyatnostcy i Pim, 26 (1981), p.584-590. Zbl0466.60007MR627864
4. [4] J. Elton, A law of large numbers for identically distributed martingale differences, Ann. Probability9(1981), p.405-412. Zbl0463.60039MR614626
5. [5] A. Gut and K.D. Schmidt, Amarts and set function processesLecture Notes in Math. 1042, Springer-Verlag1983. Zbl0525.60055MR727477
6. [6] Krengel U. and L. Sucheston, On semiamarts, amarts and processes with finite value, Advances in Prob.4 (1978), p. 197-266. MR515432
7. [7] Dinh Quang Luu, On the class of all processes having a Riesz decomposition, Acta Math. Vietnam. T.6, n.1, (1981), p. 101-107. Zbl0605.60053MR683327
8. [8] Dinh Quang Luu, Representation theorems for multivalued (regular) L1-amarts, Math. Scand.58 (1986), p. 5-22. Zbl0626.60042MR845483
9. [9] J. Neveu, Discrete parameter martingales, North-Holland Publ. Co.1975. Zbl0345.60026MR402915
10. [10] G. Pisier, Martingales with values in uniformly convex spaces, Israel J. Math.20 (1975), p. 226-250. Zbl0344.46030MR394135
11. [11] L. Schwartz, Geometry and probability in Banach spaces, Lecture Notes in Math. 852, Springer-Verlag1981. Zbl0462.46008MR612976
12. [12] J. Szulga, On the Lr-convergence, r > 0, for n-1/r Sn in Banach spaces, Bull. Acad. Polon. Sci.25 (1977), p.1011-1013. Zbl0362.60071MR482923
13. [13] J.M. Talagrand, Some structure results for martingales in the limit and pramarts, Ann. Probability13 (1985), p. 1192-1203. Zbl0582.60055MR806217
14. [14] R.L. Taylor, Stochastic convergence of weighted sums of random elements in linear spaces, Lecture Notes in Math. 672, Springer-Verlag1978. Zbl0443.60004MR513422
15. [15] X.C. Wang and M.B. Rao, Some results on the convergence of weighted sums of random elements in Banach spaces, Studia Math., 86 (1987), p.131-153. Zbl0629.60013MR901906
16. [16] W.A. Woyczynski, Asymptotic behaviour of martingales in Banach spaces, Lecture Notes in Math. 526 (1976), 273-284. Zbl0379.60045MR451394
17. [17] -----, On Marcinkiewicz-Zygmund laws of large numbers in Banach spaces and related rates of convergence, Probab. and Math. Statistics1 (1980), 117-131. Zbl0502.60006MR626306
18. [18] -----, Asymptotic behaviour of martingales in Banach spaces II, Lecture Notes in Math. 939 (1982), 216-225. Zbl0495.60012MR668549