Monthly Archives: November 2012

Van Lambalgen’s Theorem and Radon-Nikodym derivative

News
26 Oct 2012, the slides were uploaded.

Title
Van Lambalgen’s Theorem and Radon-Nikodym derivative

Type
Young Logician’s Gathering in Japan
23-25 Nov 2012
Nara Seisyounen Kaikan

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The law of the iterated logarithm in game-theoretic probability

News
15 Nov 2012, the revised slides were uploaded.
26 Oct 2012, the slides were uploaded.

Title
The law of the iterated logarithm in game-theoretic probability

Type
Fourth Workshop on Game-Theoretic Probability and Related Topics
12-14 Nov 2012
The University of Tokyo

Abstract
The Kolmogorov law of the iterated logarithm (LIL) (1929) provides the exact speed of the convergence of the sum of independent ran- dom variables under a condition. Subsequently, Hartman and Wintner (1941) showed that, in the case of i.i.d. random variables, the existence of a second moment is sufficient for the LIL. Shafer and Vovk (2001)
studied the Kolmogorov LIL in game-theoretic probability and asked the treatment of the Hartman and Winter LIL in game-theoretic prob- ability.
I present a new sufficient condition for the LIL in game-theoretic probability, which has a similar form to the Hartman and Winter LIL. The main idea is to add a little stronger hedges. This is the joint work with Akimich Takemura.

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An introduction to algorithmic randomness

News
15 Nov 2012, the revised slides were uploaded.
26 Oct 2012, the slides were uploaded.

Title
An introduction to algorithmic randomness

Type
Fourth Workshop on Game-Theoretic Probability and Related Topics
12-14 Nov 2012
The University of Tokyo

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Slides

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