Game-theoretic versions of strong law of large numbers for unbounded variables
Probability
2007-08-27 v1
Abstract
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.
Keywords
Cite
@article{arxiv.math/0603184,
title = {Game-theoretic versions of strong law of large numbers for unbounded variables},
author = {Masayuki Kumon and Akimichi Takemura and Kei Takeuchi},
journal= {arXiv preprint arXiv:math/0603184},
year = {2007}
}