Displaying similar documents to “On the history of martingales in the study of randomness.”

My encounters with martingales.

Krickeberg, Klaus (2009)

Journal Électronique d'Histoire des Probabilités et de la Statistique [electronic only]

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The notion of randomness from Aristotle to Poincaré

O. B. Sheynin (1991)

Mathématiques et Sciences Humaines

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Aristotle and even earlier scientist and philosophers attempted to define, or at least to through light upon randomness. The author sketches the attempts to direct concept of randomness into the realm of mathematical science from Aristotle up to Poincaré. He dwells on the various interpretations of randomness that were pronounced in natural science and philosophy, and on the interrelation between necessity and randomness.

Kolmogorov complexity, pseudorandom generators and statistical models testing

Jan Šindelář, Pavel Boček (2002)

Kybernetika

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An attempt to formalize heuristic concepts like strings (sequences resp.) “typical” for a probability measure is stated in the paper. Both generating and testing of such strings is considered. Kolmogorov complexity theory is used as a tool. Classes of strings “typical” for a given probability measure are introduced. It is shown that no pseudorandom generator can produce long strings from the classes. The time complexity of pseudorandom generators with oracles capable to recognize “typical”...