Abstract:
A scheme of finitely dependent (and, generally speaking, nonstationary) distribution of particles in a countable collection of cells is considered. Sufficient conditions are given for asymptotic normality of the random variables μr (the number of cells containing exactly r particles each), μ (the number of occupied cells), and ξr (the number of r-fold repetitions). For μr these conditions correspond to the “left intermediate domain of variation of the parameters”, while for ξr they include also the “central domain”. The method of moments is used in the proof.
Bibliography: 6 titles.
Citation:
V. G. Mikhailov, “Asymptotic normality in a scheme of finitely dependent distribution of particles in cells”, Math. USSR-Sb., 47:2 (1984), 499–512
\Bibitem{Mik82}
\by V.~G.~Mikhailov
\paper Asymptotic normality in a scheme of finitely dependent distribution of particles in cells
\jour Math. USSR-Sb.
\yr 1984
\vol 47
\issue 2
\pages 499--512
\mathnet{http://mi.mathnet.ru/eng/sm2897}
\crossref{https://doi.org/10.1070/SM1984v047n02ABEH002655}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=682496}
\zmath{https://zbmath.org/?q=an:0538.60015|0508.60020}
Linking options:
https://www.mathnet.ru/eng/sm2897
https://doi.org/10.1070/SM1984v047n02ABEH002655
https://www.mathnet.ru/eng/sm/v161/i4/p509
This publication is cited in the following 7 articles:
M. I. Tikhomirova, V. P. Chistyakov, “Asymptotic normality of numbers of non-occurring values of m-dependent random variables”, Discrete Math. Appl., 24:5 (2014), 305–317
V. P. Chistyakov, “Asymptotic normality of the number of values of m-dependent random variables which occur a given number of times”, Discrete Math. Appl., 21:1 (2011), 23–37
M. I. Tikhomirova, V. P. Chistyakov, “Asimptoticheskaya normalnost chisla nepoyavivshikhsya znachenii m-zavisimykh sluchainykh velichin”, Matem. vopr. kriptogr., 2:1 (2011), 119–129
A. M. Shoitov, “The compound Poisson distribution of the number of matches of values of a discrete function of s-tuples in segments of a sequence of random variables”, Discrete Math. Appl., 17:3 (2007), 209–230
A. L. Rukhin, “Pattern correlation matrices for Markov sequences and tests of randomness”, Theory Probab. Appl., 51:4 (2007), 663–679
A. M. Shoitov, “The Poisson approximation for the number of matches of values of a discrete function from chains”, Discrete Math. Appl., 15:3 (2005), 241–254
V. G. Mikhailov, A. M. Shoitov, “Structural equivalence of s-tuples in random discrete sequences”, Discrete Math. Appl., 13:6 (2003), 541–568
Citation in format AMSBIB
Contact us: