science forum beginner
Joined: 05 Jan 2006
|Posted: Sat Jul 15, 2006 7:15 pm Post subject:
convergence of probability measures
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