A moment problem for random discrete measures

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:125

Article

Kondratiev, Yuri G.^1,2  Kuna, Tobias³  Lytvynov, Eugene⁴ 

[1] Univ Bielefeld, Fak Math, D-33501 Bielefeld, Germany

[2] NPU, Kiev, Ukraine

[3] Univ Reading, Dept Math, Reading RG6 6AX, Berks, England

[4] Swansea Univ, Dept Math, Swansea SA2 8PP, W Glam, Wales

关键词: Discrete random measure;    Moment problem;    Point process;    Random measure;   

DOI  :  10.1016/j.spa.2015.03.007

来源: Elsevier

【 摘 要 】

Let X be a locally compact Polish space. A random measure on X is a probability measure on the space of all (nonnegative) Radon measures on X. Denote by K(X) the cone of all Radon measures n on X which are of the form eta = Sigma(i) s(i)delta(xi), where, for each i, s(i) > 0 and delta(xi) is the Dirac measure at x(i) is an element of X. A random discrete measure on X is a probability measure on K(X). The main result of the paper states a necessary and sufficient condition (conditional upon a mild a priori bound) when a random measure kt is also a random discrete measure. This condition is formulated solely in terms of moments of the random measure mu. Classical examples of random discrete measures are completely random measures and additive subordinators, however, the main result holds independently of any independence property. As a corollary, a characterization via moments is given when a random measure is a point process. (C) 2015 Elsevier B.V. All rights reserved.

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