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Teor. Veroyatnost. i Primenen., 2000, Volume 45, Issue 2, Pages 312–327 (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

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.

DOI: https://doi.org/10.4213/tvp465

Full text: PDF file (718 kB)

English version:
Theory of Probability and its Applications, 2001, 45:2, 233–245

Bibliographic databases:

Received: 17.07.1997
Revised: 11.11.1998
Language:

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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\jour Theory Probab. Appl.
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