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Teoriya Veroyatnostei i ee Primeneniya, 2000, Volume 45, Issue 2, Pages 312–327
DOI: https://doi.org/10.4213/tvp465 (Mi tvp465) 		 
Purely game-theoretic random sequences: II. Limiting empirical distributions and strong central limit theorem

M. Minozzo

University of Perugia, Department of Statistical Sciences, Italy
Full-text PDF (718 kB)
DOI: https://doi.org/10.4213/tvp465
Abstract: In Part I of this paper [M. Minozzo, Theory Probab. Appl., 44 (1999), pp. 511–522] a definition of typical sequences was given, without using any Kolmogorovian probability distribution $P$, by applying the principle of the excluded gambling strategy directly to a sequence of measurable functions. In this paper we forward this theory by deriving for these typical sequences some elementary limiting empirical distribution functions and some strong central limit theorem type results for the coin tossing process.
Keywords: algorithmic probability theory, almost sure limit theorems, distributions of the values, martingales, typical sequences.
Received: 17.07.1997
Revised: 11.11.1998
English version:
Theory of Probability and its Applications, 2001, Volume 45, Issue 2, Pages 233–245
DOI: https://doi.org/10.1137/S0040585X97978191
Bibliographic databases:
Language: English
Citation: M. Minozzo, “Purely game-theoretic random sequences: II. Limiting empirical distributions and strong central limit theorem”, Teor. Veroyatnost. i Primenen., 45:2 (2000), 312–327; Theory Probab. Appl., 45:2 (2001), 233–245
Citation in format AMSBIB
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