Friends, those who are into these things. I am thinking that Brownian Motion is Markov & is also a Martingale but I am struggling to conclude about the Ergodicity. If Brownian motion is not Ergodic, then we need to rethink a suitable model for stock prices when considering longer time frames. This can have an effect on the pricing of Derivatives, for example the prices of Out of the Money Put Options can be zero.

Any takers?