On a Characteryzation of Stability in Renyi's Sense in terms of weak convergence of random sequences

Author
Sylwia Rudecka, Wiesław Zięba
Institute of Mathematics, Maria Curie-Skłodowska University Plac Marii Curie-Skłodowskiej 1 20-031 Lublin, POLAND
Abstract
The aim of this note is to give a criterion of the stability of random elements in terms of convergence in law of sequences of random elements with random indices.
Keywords
stability, random elements, convergence in law, sequences, random indices
DOI
doi:10.30970/ms.6.1.153-156
Reference
1. Aldous D.J. and Eagleson G.K. On mixing and stability of limit theorems // Ann. Probability. V.6. 1978. P.325–331.

2. Billingsley P. Convergence of probability measures, – New York, 1968.

3. Csorgo M. and Fischler R. Departure from independence: the strong law, standard and random-sum central limit theorems // Acta Math. Acad. Sci. Hung. V.21. 1970. P.105–114.

4. Dobruschin R. L. Lemma o predele sloznoj sluchajnoj funkcyi // Usp. Math. Nauk. V.10. 1955. ¹2(64). P.157–159.

5. Loeve M. Probability Theory, – New-York, 1963.

6. Renyi A. On stable sequence of events // Sankhya. Ser. A. V.25. 1963. P.293–302.

7. Skorohod A. W. Predelnye teoremy dla sluchajnyh procesov // Teor. Wier. i ee primen. 1956. V.1. ¹3, P.289–319.

8. Szynal D. and Zi eba W. On some properties of the stable sequence of random elements // Publ. Math. (Debrecen). 1986. V.33. P.271–282.

9. Zi eba W. On some criterion of convergence in probability // Probability and Math. Stat. 1985. V.6. fasc.2. P.225–232. Institute of Mathematics, Maria Curie-Sk odowska University Plac Marii Curie Sk odowskiej 1 20-031 Lublin, POLAND

Pages
153-156
Volume
6
Issue
1
Year
1996
Journal
Matematychni Studii
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