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The law of the iterated logarithm in game-theoretic probability with quadratic and stronger hedges

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  • Miyabe, Kenshi
  • Takemura, Akimichi

Abstract

We prove both the validity and the sharpness of the law of the iterated logarithm in game-theoretic probability with quadratic and stronger hedges.

Suggested Citation

  • Miyabe, Kenshi & Takemura, Akimichi, 2013. "The law of the iterated logarithm in game-theoretic probability with quadratic and stronger hedges," Stochastic Processes and their Applications, Elsevier, vol. 123(8), pages 3132-3152.
    • Handle: RePEc:eee:spapps:v:123:y:2013:i:8:p:3132-3152
    DOI: 10.1016/j.spa.2013.03.018
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    References listed on IDEAS

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    1. Shin-ichiro Takazawa, 2012. "Exponential inequalities and the law of the iterated logarithm in the unbounded forecasting game," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(3), pages 615-632, June.
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    Cited by:

    1. Sato, Ryosuke & Miyabe, Kenshi & Takemura, Akimichi, 2018. "Relation between the rate of convergence of strong law of large numbers and the rate of concentration of Bayesian prior in game-theoretic probability," Stochastic Processes and their Applications, Elsevier, vol. 128(5), pages 1466-1484.

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