WEAK CONVERGENCE OF COMPOUND PROBABILITY MEASURES ON UNIFORM SPACES

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Published: Dec 1, 1999
DOI: https://doi.org/10.5556/j.tkjm.30.1999.4233
Keywords:
Uniform equicontinuity transition probability compound probability measure Gaussian transition probability

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JUN KAWABE
Department of Mathematics, Faculty of Engineering, Shinshu University, 4-17-1 Wakasato, Nagano 380-8553, Japan.

Abstract




We obtain a convergence theorem of compound probability measures on a uniform space for a net of uniformly equicontinuous transition probabilities. This theorem contains convergence theorems of product or convolution measures. We also show that for Gaussian transition probabilities on a Hilbert spaces, our assumptions in the convergence theorem can be expressed in terms of mean and covariance functions.




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How to Cite
KAWABE, J. (1999). WEAK CONVERGENCE OF COMPOUND PROBABILITY MEASURES ON UNIFORM SPACES. Tamkang Journal of Mathematics, 30(4), 271–288. https://doi.org/10.5556/j.tkjm.30.1999.4233
Issue
Vol. 30 No. 4 (1999)
Section
Papers
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