A moment problem for random discrete measures

Kondratiev Y, Kuna T, Lytvynov E (2015)
Stochastic Processes and their Applications 125(9): 3541-3569.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Kondratiev, YuriUniBi; Kuna, Tobias; Lytvynov, Eugene
Abstract / Bemerkung
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.
Stichworte
Discrete random measure; Moment problem; Random measure; Point process
Erscheinungsjahr
2015
Zeitschriftentitel
Stochastic Processes and their Applications
Band
125
Ausgabe
9
Seite(n)
3541-3569
ISSN
0304-4149
Page URI
https://pub.uni-bielefeld.de/record/2764286

Zitieren

Kondratiev Y, Kuna T, Lytvynov E. A moment problem for random discrete measures. Stochastic Processes and their Applications. 2015;125(9):3541-3569.
Kondratiev, Y., Kuna, T., & Lytvynov, E. (2015). A moment problem for random discrete measures. Stochastic Processes and their Applications, 125(9), 3541-3569. doi:10.1016/j.spa.2015.03.007
Kondratiev, Y., Kuna, T., and Lytvynov, E. (2015). A moment problem for random discrete measures. Stochastic Processes and their Applications 125, 3541-3569.
Kondratiev, Y., Kuna, T., & Lytvynov, E., 2015. A moment problem for random discrete measures. Stochastic Processes and their Applications, 125(9), p 3541-3569.
Y. Kondratiev, T. Kuna, and E. Lytvynov, “A moment problem for random discrete measures”, Stochastic Processes and their Applications, vol. 125, 2015, pp. 3541-3569.
Kondratiev, Y., Kuna, T., Lytvynov, E.: A moment problem for random discrete measures. Stochastic Processes and their Applications. 125, 3541-3569 (2015).
Kondratiev, Yuri, Kuna, Tobias, and Lytvynov, Eugene. “A moment problem for random discrete measures”. Stochastic Processes and their Applications 125.9 (2015): 3541-3569.

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