Lévy's modulus of continuity theorem
Lévy's modulus of continuity theorem is a theorem that gives a result about an almost sure behaviour of an estimate of the modulus of continuity for Wiener process, that is used to model what's known as Brownian motion.
Lévy's modulus of continuity theorem is named after the French mathematician Paul Lévy.Let be a standard Wiener process. Then, almost surely,
In other words, the sample paths of Brownian motion have modulus of continuity
with probability one, and for sufficiently small.
