STABLE AND SEMISTABLE PROBABILITY MEASURES ON CONVEX CONE

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.

Operator semistable probability measures on a Hilbert space: Corrigenda

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Operator semistable probability measures on a Hilbert space

A characterization of the class of operator semistable probability measures on a real separable Hilbert space is given.