Game-theoretic Brownian motion
arXiv:0801.1309
Abstract
This paper suggests a perfect-information game, along the lines of Levy's characterization of Brownian motion, that formalizes the process of Brownian motion in game-theoretic probability. This is perhaps the simplest situation where probability emerges in a non-stochastic environment.
17 pages
References in corpus (4)
- Continuous-time trading and the emergence of probability
- On a simple strategy weakly forcing the strong law of large numbers in the bounded forecasting game
- Game-theoretic versions of strong law of large numbers for unbounded variables
- Implications of contrarian and one-sided strategies for the fair-coin game
Cited by in corpus (4)
- Continuous-time trading and the emergence of probability
- A new formulation of asset trading games in continuous time with essential forcing of variation exponent
- Continuous-time trading and emergence of randomness
- Multistep Bayesian strategy in coin-tossing games and its application to asset trading games in continuous time