UNIFORM TIGHTNESS FOR TRANSITION PROBABILITIES
Keywords:Transition probability, compound probability measure, upper semicontinuous, set-valued mapping, uniform tighness, Gaussian, nuclear space
The aim of this paper is to give a notion of uniform tightness for transition probabilities on topological spaces, which assures the uniform tightness of compound probability measures. Then the upper semicontinuity of set-valued mappings are used in essence. As an important example, the uniform tightness for Gaussian transition probabilities on the strong dual of a nuclear real Frechet space is studied. It is also shown that some of our results contain well-known results concerning the uniform tightness and the weak convergence of probability measures.
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