Limit Theorems

One of the simplest limit theorems of game-theoretic probability is the strong law of large numbers for bounded observations. Several other results are described in [Shafer Vovk 2010], such as:

  • Kolmogorov's strong law of large numbers (Chapter 3)
  • Kolmogorov's law of the iterated logarithm (Chapter 5)
  • Lindeberg's central limit theorem (Chapter 7)
  • Finance-theoretic strong law of large numbers (Chapter 15)
  • Finance-theoretic strong law of the iterated logarithm (Chapter 15)

Many other game-theoretic limit theorems have been established by Akimichi Takemura and his school and by Shin-Ichiro Takazawa.

Bibliography