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Invariance principle for numbers of particles in cells of a general allocation scheme
I. Fazekasa, A. N. Chuprunovb a University of Debrecen
b Chuvash State University
Abstract:
Let η1,…ηN be a generalized allocation scheme of n particles over N cells defined by independent random variables ξ1,…,ξN having power series distribution with parameter β. Denote by m(β) and σ2(β) an expectation and a variance of ξi. Let β be such that nN=m(β). We consider random processes Xn,N(t)=∑[tN]i=1ηi and Yn,N(t)=n−1/2(Xn,N(t)−[tN]nN), 0⩽t⩽1. We find conditions under which for n,N→∞ the random processes σ−1(β)√nNYn,N converge in distribution in the Skhorohod space to a Brounian bridge, and conditions ubder which for fixes n and N→∞ the random processes Xn,N converge in distribution in the Skhorohod space to nFn, where Fn is an empirical process.
Keywords:
invariance principle, generalized allocation scheme, Poisson limit theorem, local limit theorem, empirical process, Brownian bridge.
Received: 12.09.2022
Citation:
I. Fazekas, A. N. Chuprunov, “Invariance principle for numbers of particles in cells of a general allocation scheme”, Diskr. Mat., 35:3 (2023), 81–99
Linking options:
https://www.mathnet.ru/eng/dm1738https://doi.org/10.4213/dm1738 https://www.mathnet.ru/eng/dm/v35/i3/p81
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Abstract page: | 170 | Full-text PDF : | 22 | References: | 32 | First page: | 8 |
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