convergence of probability measures

pkg · science forum beginner Joined: 05 Jan 2006 Posts: 30

Dear all,
let S_n(t), n \in IN, and S(t) be semigroups of a Markov processes with
S_n(t) f --> S(t) f if n --> \infty. (*)
If this holds for a suitably large class of functions f, the respective
Markov processes converge in finite dimensional distributions.
Usually one uses tightness to infer convergence in distr. on path space
from convergence in f.d.d..
My question is:
If I know that the convergence in (*) is uniform in t \in [0,T], is it
then possible to conclude that I even have convergence in distribution
on the path space of the markov processes restricted to the finite time
interval [0,T].
BR
pkg

Google