The French mathematician Paul Lévy proved the following theorem, which gives a necessary and sufficient condition for a continuous -valued stochastic process to actually be -dimensional Brownian motion. Hence, Lévy's condition can actually be used as an alternative definition of Brownian motion.
The French mathematician Paul Lévy proved the following theorem which gives a necessary and sufficient condition for a continuous -valued stochastic process to a,ctually be -dimensional Brownian motion. Hence, Lévy's condition can actually be used as an alternative definition of Brownian motion.