×

A general principle for limit theorems in finitely additive probability. (English) Zbl 0507.60012


MSC:

60F05 Central limit and other weak theorems
60G07 General theory of stochastic processes
60G40 Stopping times; optimal stopping problems; gambling theory
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] D. J. Aldous, Limit theorems for subsequences of arbitrarily-dependent sequences of random variables, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 40 (1977), no. 1, 59 – 82. · Zbl 0571.60027 · doi:10.1007/BF00535707
[2] Patrick Billingsley, Convergence of probability measures, John Wiley & Sons, Inc., New York-London-Sydney, 1968. · Zbl 0271.60009
[3] Leo Breiman, Probability, Addison-Wesley Publishing Company, Reading, Mass.-London-Don Mills, Ont., 1968. · Zbl 0174.48801
[4] Robert Chen, A finitely additive version of Kolmogorov’s law of the iterated logarithm, Israel J. Math. 23 (1976), no. 3-4, 209 – 220. · Zbl 0367.60027 · doi:10.1007/BF02761801
[5] Robert Chen, On almost sure convergence in a finitely additive setting, Z. Wahrsch. Verw. Gebiete 37 (1976/77), no. 4, 341 – 356. · Zbl 0331.60010 · doi:10.1007/BF00533425
[6] Lester E. Dubins, On Lebesgue-like extensions of finitely additive measures, Ann. Probability 2 (1974), 456 – 463. · Zbl 0288.28010
[7] Lester E. Dubins and Leonard J. Savage, How to gamble if you must. Inequalities for stochastic processes, McGraw-Hill Book Co., New York-Toronto-London-Sydney, 1965. · Zbl 0359.60002
[8] Michel Loève, Probability theory, Third edition, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1963. · Zbl 0095.12201
[9] Jacques Neveu, Mathematical foundations of the calculus of probability, Translated by Amiel Feinstein, Holden-Day, Inc., San Francisco, Calif.-London-Amsterdam, 1965. · Zbl 0137.11301
[10] Roger A. Purves and William D. Sudderth, Some finitely additive probability, Ann. Probability 4 (1976), no. 2, 259 – 276. · Zbl 0367.60034
[11] S. Ramakrishnan, Central limit theorems in a finitely additive setting, Illinois J. Math. 28 (1984), no. 1, 139 – 161. · Zbl 0514.60030
[12] V. Strassen, An invariance principle for the law of the iterated logarithm, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 3 (1964), 211 – 226 (1964). · Zbl 0132.12903 · doi:10.1007/BF00534910
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.