- Autor
- Berkes, István
- Tichy, Robert
- TitelLacunary series and stable distributions
- Datei
- DOI10.1007/978-3-319-12442-1_2
- Erschienen inMathematical Statistics and Limit Theorems
- Erscheinungsjahr2015
- Seiten7-19
- LicenceCC BY
- ISBN978-3-319-12442-1
- Download Statistik2022
- Peer ReviewJa
- AbstractBy well-known results of probability theory, any sequence of random variables with bounded second moments has a subsequence satisfying the central limit theorem and the law of the iterated logarithm in a randomized form. In this paper we give criteria for a sequence \((X_n)\) of random variables to have a subsequence \((X_{n_k})\) whose weighted partial sums, suitably normalized, converge weakly to a symmetric stable distribution with parameter \(0<\alpha <2\).
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