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On the Levy-Baxter theorems for shot-noise fields. I

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Abstract

We consider shot-noise fields generated by countably additive stochastically continuous homogeneous random measures with independent values on disjoint sets. We establish necessary and sufficient conditions under which the shot-noise fields possess the Levy-Baxter property on fixed and increasing parametric sets.

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Authors and Affiliations

  1. Kiev Polytechnic Institute, Kiev

    V. V. Buldygin, V. M. Mel’nik & V. G. Shportyuk

Authors
  1. V. V. Buldygin
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  2. V. M. Mel’nik
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  3. V. G. Shportyuk
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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 11, pp. 1463–1476, November, 1998.

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Buldygin, V.V., Mel’nik, V.M. & Shportyuk, V.G. On the Levy-Baxter theorems for shot-noise fields. I. Ukr Math J 50, 1671–1685 (1998). https://doi.org/10.1007/BF02524474

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  • DOI: https://doi.org/10.1007/BF02524474

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