The Borel-Cantelli lemmas, probability laws and Kolmogorov complexity

DOI10.1214/aop/1015345756zbMath1017.60002OpenAlexW1571949533WikidataQ124817095 ScholiaQ124817095MaRDI QIDQ1872229

George Davie

Publication date: 6 May 2003

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aop/1015345756

zbMATH Keywords

Kolmogorov complexityprobability laweffective Borel-Cantelli lemmasKolmogorov-Chejtin random sequenceMartin-Löf random sequence

Mathematics Subject Classification ID

Algorithmic information theory (Kolmogorov complexity, etc.) (68Q30) Axioms; other general questions in probability (60A05)

Related Items (11)

Constraints placed on random sequences by their compressibility ⋮ The descriptive complexity of stochastic integration ⋮ Revisiting Chaitin's incompleteness theorem ⋮ On the computability of a construction of Brownian motion ⋮ An Application of Martin-Löf Randomness to Effective Probability Theory ⋮ Algorithmically random series and Brownian motion ⋮ The law of the iterated logarithm for a class of SPDEs ⋮ Polynomial time relatively computable triangular arrays for almost sure convergence ⋮ A computable version of the random signs problem and Kolmogorov complexity ⋮ Unnamed Item ⋮ Computable Measure Theory and Algorithmic Randomness

Cites Work

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• The Law of the Iterated Logarithm for Random Kolmogorov, or Chaotic, Sequences
• Algorithmic Information Theory
• A Theory of Program Size Formally Identical to Information Theory

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