Blumenthal's zero–one law
In the mathematical theory of probability, Blumenthal's zero–one law, named after Robert McCallum Blumenthal, is a statement about the nature of the beginnings of right continuous Feller process. Loosely, it states that any right continuous Feller process on starting from deterministic point has also deterministic initial movement.Statement
Suppose that is an adapted right continuous Feller process on a probability space such that is constant with probability one. Let. Then any event in the germ sigma algebra has either orGeneralization
Suppose that is an adapted stochastic process on a probability space such that is constant with probability one. If has Markov property with respect to the filtration then any event has either or Note that every right continuous Feller process on a probability space has strong Markov property with respect to the filtration.
