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2014 | OriginalPaper | Chapter

17. On the Regularities of Mass Random Phenomena

Authors : Victor I. Ivanenko, Valery A. Labkovsky

Published in: Continuous and Distributed Systems

Publisher: Springer International Publishing

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Abstract

This note presents a not very well known result concerning the frequentist origins of probability. This result provides a positive answer to the question of existence of statistical regularities of so called random in a broad sense mass phenomena, using the terminology of A. N. Kolmogorov [20]. It turns out, that some closed in weak-\(*\) topology family of finitely-additive probabilities plays the role of the statistical regularity of any such phenomenon. If the mass phenomenon is stochastic, then this family degenerates into a usual countably-additive probability measure. The note provides precise definitions, the formulation and the proof of the theorem of existence of statistical regularities, as well as the examples of their application.

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previous chapter On Global Attractors for Autonomous Damped Wave Equation with Discontinuous Nonlinearity

next chapter Optimality Conditions for Partially Observable Markov Decision Processes

Remark that the term “nonstochastic” appeared in [27] in the context of Kolmogorov’s complexity, meaning “more complex than stochastic”. In this chapter the meaning of this term is “more random than stochastic”.

I am thankful to professor Vladimir Vovk who made me familiar with the works of professor Terrence Fine and, in particular, with this chapter.

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Title: On the Regularities of Mass Random Phenomena
Authors: Victor I. Ivanenko
Valery A. Labkovsky
Publisher: Springer International Publishing
Book: Continuous and Distributed Systems
Print ISBN: 978-3-319-03145-3

Electronic ISBN: 978-3-319-03146-0

Copyright Year: 2014
DOI: https://doi.org/10.1007/978-3-319-03146-0_17