# 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

- Glenn Shafer and Vladimir Vovk.
*Probability and finance: It's only a game!*. New York: Wiley, 2001.