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STABLE AND SEMISTABLE PROBABILITY MEASURES ON CONVEX CONE

Published online by Cambridge University Press:  20 November 2014

NAM BUI QUANG
Affiliation:
Academy of Antiaircraft and Air Forces, Son Tay Town, Ha Noi, Vietnam email [email protected]
PHUC HO DANG*
Affiliation:
Institute of Mathematics, VAST, 18 Hoang Quoc Viet, Ha Noi, Vietnam email [email protected]
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Abstract

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The study concerns semistability and stability of probability measures on a convex cone, showing that the set $S(\boldsymbol{{\it\mu}})$ of all positive numbers $t>0$ such that a given probability measure $\boldsymbol{{\it\mu}}$ is $t$-semistable establishes a closed subgroup of the multiplicative group $R^{+}$; semistability and stability exponents of probability measures are positive numbers if and only if the neutral element of the convex cone coincides with the origin; a probability measure is (semi)stable if and only if its domain of (semi-)attraction is not empty; and the domain of attraction of a given stable probability measure coincides with its domain of semi-attraction.

Type
Research Article
Copyright
© 2014 Australian Mathematical Publishing Association Inc. 

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