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A general theorem on the limit behavior of superpositions of independent random processes with applications to Cox processes

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Abstract

A general theorem is presented which gives necessary and sufficient conditions of the convergence of one-dimensional distributions of appropriately centered and normalized superpositions of independent stochastic processes. This theorem is used as a tool for obtaining limit theorems for doubly stochastic Poisson processes (Cox processes).

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Authors and Affiliations

  1. Department of Computational Mathematics and Cybernetics, Moscow State University, Vorob'yovy Gory, 118899, Moscow, Russia

    V. Y. Korolev

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  1. V. Y. Korolev
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Additional information

Supported in part by the Russian Foundation for Fundamental Research (grant No. 93-01-01446) and also by the International Science Foundation and the government of Russia (projects NFW000 and NFW300).

Proceedings of the XVII Seminar on Stability Problems for Stochastic Models, Kazan, Russia, 1995, Part I.

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Korolev, V.Y. A general theorem on the limit behavior of superpositions of independent random processes with applications to Cox processes. J Math Sci 81, 2951–2956 (1996). https://doi.org/10.1007/BF02362504

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  • DOI: https://doi.org/10.1007/BF02362504

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