无界变量强大数律的博弈论形式
Game-theoretic versions of strong law of large numbers for unbounded variables
摘要：
我们在Shafer和Vovk（2001）的博弈论概率框架下考虑了强大数律（SLLN）。我们证明了几个版本的SLLN的情况下，现实的举动是无界的。我们的博弈论版本的SLLN在很大程度上对应于标准的测量理论的结果。然而，博弈论的证明是不同的明确考虑各种模糊限制语的测量理论。在测度论的证明存在的时刻，而在我们的博弈论的证明，我们假设各种对冲有限的价格怀疑论者的可用性。
英文摘要：
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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