On the equidistribution of sums of independent random variables
HTML articles powered by AMS MathViewer
- by Herbert Robbins
- Proc. Amer. Math. Soc. 4 (1953), 786-799
- DOI: https://doi.org/10.1090/S0002-9939-1953-0056869-7
- PDF | Request permission
References
- W. Feller, Probability theory and its applications, vol. 1, New York, 1950.
- Hermann Weyl, Über die Gleichverteilung von Zahlen mod. Eins, Math. Ann. 77 (1916), no. 3, 313–352 (German). MR 1511862, DOI 10.1007/BF01475864 H. Poincaré, Calcul des probabilités, Paris, 1896. M. Fréchet, Méthode des fonctions arbitraires, etc., vol. 1 (Part III, Book 2 of Traité du calcul des probabilités (Borel)), Paris, 1938. B. Hostinský, Méthodes générales du calcul des probabilités (Part LII of Mémorial des sciences mathématiques), Paris, 1931.
- P. Erdös and M. Kac, On the number of positive sums of independent random variables, Bull. Amer. Math. Soc. 53 (1947), 1011–1020. MR 23011, DOI 10.1090/S0002-9904-1947-08928-X G. Kallianpur and H. Robbins, On the sequence of sums of independent random variables, unpublished.
- Françoise Ulam, Nonmathematical reminiscences about Johnny von Neumann, The legacy of John von Neumann (Hempstead, NY, 1988) Proc. Sympos. Pure Math., vol. 50, Amer. Math. Soc., Providence, RI, 1990, pp. 9–13. MR 1067746, DOI 10.1090/pspum/050/1067746
- Shizuo Kakutani, Random ergodic theorems and Markoff processes with a stable distribution, Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, 1950, University of California Press, Berkeley-Los Angeles, Calif., 1951, pp. 247–261. MR 0044773 E. R. van Kampen, Almost periodic functions and compact groups, Ann. of Math. (2) vol. 37 (1936) pp. 48-91. A. Weil, Sur les fonctions presque périodiques de v. Neumann, C. R. Acad. Sci. Paris vol. 200 (1935) pp. 38-40. P. Lévy, L’addition des variables aléatoires définies sur une circonférence, Bull. Soc. Math. France vol. 67 (1939) pp. 1-41.
- Yukiyosi Kawada and Kiyosi Itô, On the probability distribution on a compact group. I, Proc. Phys.-Math. Soc. Japan (3) 22 (1940), 977–998. MR 3462
- T. E. Harris and Herbert Robbins, Ergodic theory of Markov chains admitting an infinite invariant measure, Proc. Nat. Acad. Sci. U.S.A. 39 (1953), 860–864. MR 56873, DOI 10.1073/pnas.39.8.860
Bibliographic Information
- © Copyright 1953 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 4 (1953), 786-799
- MSC: Primary 60.0X
- DOI: https://doi.org/10.1090/S0002-9939-1953-0056869-7
- MathSciNet review: 0056869