Suppose (X t , P x ) is a Markov process with respect to a filtration {F t }. Suppose that Et ⊂ Ft for each t and that X t is Et measurable for each t. Show that (X t , P x ) is a Markov process with...

Suppose (X_t, P_x) is a Markov process with respect to a filtration {F_t}. Suppose that Et ⊂ Ft for each t and that X_t
is Et measurable for each t. Show that (X_t, P_x) is a Markov process with respect to the filtration {E_t}.

Give an example of a Markov process that is not a strong Markov process.

Chapter 21