Open AccessUNIFORM TIGHTNESS FOR TRANSITION PROBABILITIES
Author(s) -
Jun Kawabe
Publication year - 1995
Publication title -
tamkang journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.324
H-Index - 18
eISSN - 0049-2930
pISSN - 2073-9826
DOI - 10.5556/j.tkjm.26.1995.4408
Subject(s) - mathematics , gaussian , convergence (economics) , set (abstract data type) , dual (grammatical number) , space (punctuation) , probability measure , topological space , transition (genetics) , pure mathematics , topology (electrical circuits) , discrete mathematics , statistical physics , combinatorics , computer science , physics , art , literature , quantum mechanics , economics , programming language , economic growth , operating system , biochemistry , chemistry , gene
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.