Show that if A is a bounded operator and is a strongly continuous semi group of operators with infinitesimal generator A. (We cannot assert that the Tt are contractions.) Let (Xt, Px) be a Markov...

Show that if A is a bounded operator and

is a strongly continuous semi group of operators with infinitesimal generator A. (We cannot assert that the T_t
are contractions.)

Let (X_t, P^x) be a Markov process with transition probabilities given by

Determine L and D(L).