Suppose that X is a right process which is associated with a semi-Dirichlet form(ε,D(ε)) on L^2(E;m).Let J be the jumping measure of(ε,D(ε)) satisfying J(E×E-d) 0.If one of these assertions holds,then(P_t^u)t≥0 is strongly continuous on L^2(E;m).If X is equipped with a differential structure,then under some other assumptions,these conclusions remain valid without assuming J(E×E-d)<∞.Some examples are also given in this part.Let A_t be a local continuous additive functional with zero quadratic variation.In the second part,we get the representation of A_t and give two sufficient conditions for P_t^A f(x) = E_x[e^(A_t) f(X_t)]to be strongly continuous.
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