UNIFORM TIGHTNESS FOR TRANSITION PROBABILITIES

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Published: Dec 1, 1995
DOI: https://doi.org/10.5556/j.tkjm.26.1995.4408
Keywords:
Transition probability compound probability measure upper semicontinuous set-valued mapping uniform tighness Gaussian nuclear space

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JUN KAWABE
Department of Mathematics, Faculty of Engineering, Shinshu University, Wakasato, Nagano 380, Japan.

Abstract




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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How to Cite
KAWABE, J. (1995). UNIFORM TIGHTNESS FOR TRANSITION PROBABILITIES. Tamkang Journal of Mathematics, 26(4), 283–298. https://doi.org/10.5556/j.tkjm.26.1995.4408
Issue
Vol. 26 No. 4 (1995)
Section
Papers
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