On approximations to generalized Cox processes

• Autorzy: Bening V. E. , Korolev V. Yu.
• Języki publikacji: EN

Abstrakty

EN

A refined estimate of the rate of convergence of one-dimensional distributions of nonrandomly centered generalized Cox processes to location mixtures of normal laws is presented. Asymptotic expansions for these distributions are constructed. Some estimates for the concentration functions of these distributions are proved.

Słowa kluczowe

EN

Cox process; approximation of one dimensional distributions; mixtures of normal laws

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 1998
• Tom: Vol. 18, Fasc. 2
• Strony: 247--270
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Bening V. E.

• Faculty of Computational Mathematics & Cybernetics, Moscow State University, Vorobyovy Gory, Moscow, 119899, Russia

autor

Korolev V. Yu.

• Faculty of Computational Mathematics & Cybernetics, Moscow State University, Vorobyovy Gory, Moscow, 119899, Russia

Bibliografia

• [1] V. E. Bening and V. Yu. Korolev, Asymptotic behavior of generalized Cox processes, Bull. Moscow University, Ser. Comput. Math. Cybernetics No. 3 (1996), pp. 55-68.
• [2] — Limit behavior of nonrandomly centered generalized Cox processes, Fund. Appl. Math. 2, No. 4 (1996), pp. 957-975.
• [3] — and S. Ya. Shorgin, On approximations to generalized Poisson processes, J. Math. Sci. 83, No. 3 (1997), pp. 360-373.
• [4] В. V. Gnedenko and A. N. Kolmogorov, Limit Distributions for Sums of Independent Random Variables, Addison-Wesley, Reading, MA, 1954.
• [5] В. V. Gnedenko and V. Yu. Korolev, Random Summation: Limit Theorems and Applications, CRC Press, Boca Raton, Florida, 1996.
• [6] J. Grandell, Doubly Stochastic Poisson Processes, Springer, Berlin-Heidelberg-New York 1976.
• [7] V. Yu. Korolev, A general theorem on limit behavior of superpositions of independent stochastic processes with applications to Cox processes, J. Math. Sei. 81, No. 5 (1996), pp. 2951-2956.
• [8] — and S. Ya. Shorgin, On the absolute constant in the remainder term estimate in the central limit theorem for Poisson random sums, in: Probabilistic Methods in Discrete Mathematics, Proceedings of the Fourth International Petrozavodsk Conference, VSP, Utrecht, pp. 305-308.
• [9] V. M. Kruglov and V. Yu. Korolev, Limit Theorems for Random Sums (in Russian), Moscow University Press, Moscow 1990.
• [10] R. Michel, On Berry-Esseen results for the compound Poisson distribution, Insurance Math. Econom. 13, No. 1 (1986), pp. 35-37.
• [11] V. V. Petrov, Sums of Independent Random Variables, Springer, Berlin-Heidelberg-New York 1975.
• [12] V. M. Zolotarev, Modern Theory of Summation of Independent Random Variables (in Russian), Nauka, Moscow 1986.