Maybe it will be interesting to consider if all Markov processes are ergodic?one characteristic of the ergodic property of a random function is an equality means over the time and space. If observations do not present closeness means it looks difficult to expect ergodicity.
"if all Markov processes are ergodic" sounds a little bit strange. Markov processes is a big class of random processes. If some conditions are satisfied a Markov process is ergodic. It was a book about stability stochastic processes written in about 1970 by Khasminskii. It wa a chapter where Ergodic properties of SDE solutions were studied.Maybe it will be interesting to consider if all Markov processes are ergodic?one characteristic of the ergodic property of a random function is an equality means over the time and space. If observations do not present closeness means it looks difficult to expect ergodicity.
bearish, the question was about "Brownian Motion is Markov & is also a Martingale but I am struggling to conclude about the Ergodicity " is about other drama.Welcome, Edwin! I am glad you and list found each other so quickly. Could you expand slightly on your opening remark: "This can have an effect on the pricing of Derivatives, for example the prices of Out of the Money Put Options can be zero"?
If only someone could invent a worldwide, searcheable network which stored published papers by academic luminaries and was readily accessible to every student or professional in the world. Then it would be easy to answer such questions.Is Brownian Motion Ergodic?
It is more simpler question can be ask for the GBM stock model. No one care about testing. It is a basic assumption. If you can see any evidence of ergodicity in the market you can assume it if not such assumption better to reject. Long run stock market behavior much worse be predicted than weather in 5 years forward.I think the cleaner question is to ask if stock prices observed in the markets exhibit any ergodicity.