The Annals of Probability

The Borel–Cantelli Lemmas, Probability Laws and Kolmogorov Complexity

George Davie

Full-text: Open access

Abstract

We formulate effective versions of the Borel–Cantelli lemmas using a coefficient from Kolmogorov complexity. We then use these effective versions to lift the effective content of the law of large numbers and the law of the iterated logarithm.

Article information

Source
Ann. Probab., Volume 29, Number 4 (2001), 1426-1434.

Dates
First available in Project Euclid: 5 March 2002

Permanent link to this document
https://projecteuclid.org/euclid.aop/1015345756

Digital Object Identifier
doi:10.1214/aop/1015345756

Mathematical Reviews number (MathSciNet)
MR1880226

Zentralblatt MATH identifier
1017.60002

Subjects
Primary: 68Q30: Algorithmic information theory (Kolmogorov complexity, etc.) [See also 03D32] 60A05: Axioms; other general questions

Keywords
Effective Borel-Cantelli lemmas Kolmogorov complexity compressibility coefficient probability law

Citation

Davie, George. The Borel–Cantelli Lemmas, Probability Laws and Kolmogorov Complexity. Ann. Probab. 29 (2001), no. 4, 1426--1434. doi:10.1214/aop/1015345756. https://projecteuclid.org/euclid.aop/1015345756


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References

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