Game-theoretic versions of strong law of large numbers for unbounded variables

Details Game-theoretic versions of strong law of large numbers for unbounded variables Game-theoretic versions of strong law of large numbers for unbounded variables

2006-03-08

arxiv.org/abs/math/0603184v1

Stochastics, 79(5), (2007), 449-468

Mathematics

Probability

Scientific paper

10.1080/17442500701323023

We consider strong law of large numbers (SLLN) in the framework of game-theoretic probability of Shafer and Vovk (2001). We prove several versions of SLLN for the case that Reality's moves are unbounded. Our game-theoretic versions of SLLN largely correspond to standard measure-theoretic results. However game-theoretic proofs are different from measure-theoretic ones in the explicit consideration of various hedges. In measure-theoretic proofs existence of moments are assumed, whereas in our game-theoretic proofs we assume availability of various hedges to Skeptic for finite prices.

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