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STABLE AND SEMISTABLE PROBABILITY MEASURES ON CONVEX CONE
- Part of
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- Journal:
- Journal of the Australian Mathematical Society / Volume 98 / Issue 3 / June 2015
- Published online by Cambridge University Press:
- 20 November 2014, pp. 390-406
- Print publication:
- June 2015
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- Article
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- You have access
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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.
