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STABLE AND SEMISTABLE PROBABILITY MEASURES ON CONVEX CONE

Part of: Distribution theory - Probability Probability theory on algebraic and topological structures

Published online by Cambridge University Press:  20 November 2014

NAM BUI QUANG  and
PHUC HO DANG
NAM BUI QUANG
Affiliation:
Academy of Antiaircraft and Air Forces, Son Tay Town, Ha Noi, Vietnam email bqnam72@gmail.com
PHUC HO DANG*
Affiliation:
Institute of Mathematics, VAST, 18 Hoang Quoc Viet, Ha Noi, Vietnam email hdphuc@math.ac.vn
*
✉hdphuc@math.ac.vn
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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.

Keywords

convex cone(semi)stable probability measures(semi)stability exponentdomain of (semi-)attraction

MSC classification

Primary: 60E07: Infinitely divisible distributions; stable distributions
Secondary: 60B12: Limit theorems for vector-valued random variables (infinite-dimensional case)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 98 , Issue 3 , June 2015 , pp. 390 - 406
Copyright
© 2014 Australian Mathematical Publishing Association Inc. 

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