Limit theorems for measures on nonmetrizable locally compact abelian groups
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- by David C. Bossard PDF
- Trans. Amer. Math. Soc. 159 (1971), 185-205 Request permission
Abstract:
In a recent book, Parthasarathy provides limit theorems for sums of independent random variables defined on a metrizable locally compact abelian group. These results make heavy use of the metric assumption. This paper consists of a reworking of certain results contained in Parthasarathy to see what can be done without the metric restriction. Among the topics considered are: necessary and sufficient conditions for a limit law to have an idempotent factor; the relationship between limits of compound Poisson laws and limits of sums of independent random variables; and a representation theorem for certain limit laws.References
- K. R. Parthasarathy, Probability measures on metric spaces, Probability and Mathematical Statistics, No. 3, Academic Press, Inc., New York-London, 1967. MR 0226684
- B. V. Gnedenko and A. N. Kolmogorov, Limit distributions for sums of independent random variables, Addison-Wesley Publishing Co., Inc., Cambridge, Mass., 1954. Translated and annotated by K. L. Chung. With an Appendix by J. L. Doob. MR 0062975
- Yu. V. Prokhorov, Convergence of random processes and limit theorems in probability theory, Teor. Veroyatnost. i Primenen. 1 (1956), 177–238 (Russian, with English summary). MR 0084896
- K. R. Parthasarathy, R. Ranga Rao, and S. R. S. Varadhan, On the category of indecomposable distributions on topological groups, Trans. Amer. Math. Soc. 102 (1962), 200–217. MR 153041, DOI 10.1090/S0002-9947-1962-0153041-7 D. C. Bossard, Probability on locally compact abelian groups: Sums of independent random variables, Thesis, Dartmouth College, Hanover, N. H., 1967.
- Edwin Hewitt and Kenneth A. Ross, Abstract harmonic analysis. Vol. I, 2nd ed., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 115, Springer-Verlag, Berlin-New York, 1979. Structure of topological groups, integration theory, group representations. MR 551496, DOI 10.1007/978-1-4419-8638-2
- Ulf Grenander, Probabilities on algebraic structures, 2nd ed., Almqvist & Wiksell, Stockholm; John Wiley & Sons Inc., New York-London, 1968. MR 0259969
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 159 (1971), 185-205
- MSC: Primary 60.08
- DOI: https://doi.org/10.1090/S0002-9947-1971-0279845-3
- MathSciNet review: 0279845