On a Characteryzation of Stability in Renyi's Sense in terms of weak convergence of random sequences |
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| Author |
Institute of Mathematics, Maria Curie-Skłodowska University
Plac Marii Curie-Skłodowskiej 1
20-031 Lublin, POLAND
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| 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.
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| Keywords |
stability, random elements, convergence in law, sequences, random indices
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| DOI |
doi:10.30970/ms.6.1.153-156
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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
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| Volume |
6
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| Issue |
1
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| Year |
1996
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| Journal |
Matematychni Studii
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| Full text of paper | |
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