Tightness of probability measures in D([0,T];C) and D([0,T];D) (Q1084739)

The author gives tightness criteria for sequences of stochastic processes \(X^ n_ t\), \(n=1,2,..\). taking values in \(C=C(R^ d,R^ d)\) and \(D=D([0,T];C)\) with discontinuities of at most the first kind. Here C is the space of continuous maps from \(R^ d\) into itself and D is the set of all maps from [0,T] into C, right continuous with left hand limits. Then he applies these criteria to obtain a tightness condition for Levy processes with values in C and discusses the tightness of stochastic flows generated by C-valued Levy processes.