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Weak laws of large numbers for cooperative gamblers. (English) Zbl 05651903

60F05Central limit and other weak theorems
Full Text: DOI
[1] N. H. Bingham, C. M. Goldie and J. L. Teugels, Regular variation, Encyclopedia of Mathematics and its Applications 27, Cambridge University Press, Cambridge, 1987. · Zbl 0617.26001
[2] R. Bojanić and E. Seneta, Slowly varying functions and asymptotic relations, J. Math. Anal. Appl., 34 (1971), 302--315. · Zbl 0222.26003 · doi:10.1016/0022-247X(71)90114-4
[3] Y. S. Chow and H. Teicher, Almost certain summability of independent, identically distributed random variables, Ann. Math. Statist., 42 (1971), 401--404. · Zbl 0229.60022 · doi:10.1214/aoms/1177693533
[4] H. Cohn, Convergence in probability and almost sure with applications, Stochastic Processes Appl., 94 (2001), 135--154. · Zbl 1053.60092 · doi:10.1016/S0304-4149(01)00075-8
[5] H. Cohn and P. Hall, On the limit behaviour of weighted sums of random variables, Z. Wahrsch. Verw. Gebiete, 59 (1982), 319--331. · Zbl 0482.60023 · doi:10.1007/BF00532224
[6] S. Csörgo and G. Simons, Laws of large numbers for cooperative St. Petersburg gamblers, Period. Math. Hungar., 50 (2005), 99--115. · Zbl 1113.60026 · doi:10.1007/s10998-005-0005-9
[7] S. Csörgo and G. Simons, Pooling strategies for St. Petersburg gamblers, Bernoulli, 12 (2006), 971--1002. · Zbl 1130.91018 · doi:10.3150/bj/1165269147
[8] N. Etemadi, Convergence of weighted averages of random variables revisited, Proc. Amer. Math. Soc., 134 (2006), 2739--2744. · Zbl 1088.60018 · doi:10.1090/S0002-9939-06-08296-7
[9] W. Feller, An introduction to probability theory and its applications, Volume II, Wiley, New York, 1966, 2nd edition: 1971. · Zbl 0138.10207
[10] B. V. Gnedenko and A. N. Kolmogorov, Limit distributions for sums of independent random variables, Addison-Wesley, Cambridge, Massachusetts, 1954. · Zbl 0056.36001
[11] B. Jamison, S. Orey and W. Pruitt, Convergence of weighted averages of independent random variables, Z. Wahrsch. Verw. Gebiete, 4 (1965), 40--44. · Zbl 0141.16404 · doi:10.1007/BF00535481
[12] H. Kesten and R. A. Maller, Infinite limits and infinite limit points of random walks, and trimmed sums, Ann. Probab., 22 (1994), 1473--1513. · Zbl 0816.60067 · doi:10.1214/aop/1176988609
[13] P. Kevei, Generalized n-Paul paradox, Statist. Probab. Letters, 77 (2007), 1043--1049. · Zbl 1138.60026 · doi:10.1016/j.spl.2006.08.027
[14] A. Y. Khintchine, Su una legge dei grandi numeri generalizzata, Giornale dell’Istituto Italiano degli Attuari, 7 (1936), 365--377. · Zbl 0015.16701
[15] R. A. Maller, Relative stability and the strong law of large numbers, Z. Wahrsch. Verw. Gebiete, 43 (1978), 141--148. · Zbl 0366.60035 · doi:10.1007/BF00668456
[16] R. A. Maller, Relative stability, characteristic functions and stochastic compactness, J. Austral. Math. Soc. Ser. A, 28 (1979), 499--509. · Zbl 0396.60020 · doi:10.1017/S1446788700012635
[17] B. A. Rogozin, The distribution of the first ladder moment and height and fluctuation of a random walk, Theory Probab. Appl., 16 (1971), 575--595. · Zbl 0269.60053 · doi:10.1137/1116067
[18] E. Seneta, Regularly varying functions, Lecture Notes in Mathematics 508, Springer, Berlin, 1976. · Zbl 0324.26002
[19] F. T. Wright, R. D. Platt and T. Robertson, A strong law for weighted averages of independent, identically distributed random variables with arbitrary heavy tails, Ann. Probab., 5 (1977), 586--590. · Zbl 0367.60029 · doi:10.1214/aop/1176995767