A mathematical introduction to transitional lotteries

When we face a decision matter we do not face a frozen-time where all keep still while we are making a decision, but the time goes by and the probability distribution keeps moving by new available information. In this paper I want to build up the mathematical framework of a special kind of lottery: the transitional lotteries. This theory could be helpful to give to the decision theory a new key so as to dene a more accurate mental path. In orther to do that we will need a mathematical framework based upon the Kolmogorov operator which will be our transitional object, the core of this kind of lottery.