Suppose is a strong Markov process and f is a non-negative invariant function for Suppose g is a non-negative invariant function for Show that f g is a non-negative invariant function for Suppose...

Suppose

is a strong Markov process and f is a non-negative invariant function for

Suppose g is a non-negative invariant function for

Show that f g is a non-negative invariant function for

Suppose A and B are additive functionals for a Markov process and A and B have continuous paths. Prove that if

for all x and t, then

for all x.