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May 2018 Functional central limit theorems in $L^{2}(0,1)$ for logarithmic combinatorial assemblies
Koji Tsukuda
Bernoulli 24(2): 1033-1052 (May 2018). DOI: 10.3150/16-BEJ847

Abstract

Functional central limit theorems in $L^{2}(0,1)$ for logarithmic combinatorial assemblies are presented. The random elements argued in this paper are viewed as elements taking values in $L^{2}(0,1)$ whereas the Skorokhod space is argued as a framework of weak convergences in functional central limit theorems for random combinatorial structures in the literature. It enables us to treat other standardized random processes which converge weakly to a corresponding Gaussian process with additional assumptions.

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Koji Tsukuda. "Functional central limit theorems in $L^{2}(0,1)$ for logarithmic combinatorial assemblies." Bernoulli 24 (2) 1033 - 1052, May 2018. https://doi.org/10.3150/16-BEJ847

Information

Received: 1 October 2015; Published: May 2018
First available in Project Euclid: 21 September 2017

zbMATH: 06778357
MathSciNet: MR3706786
Digital Object Identifier: 10.3150/16-BEJ847

Keywords: functional central limit theorem , logarithmic assembly , Poisson approximation , Random mappings , the Ewens sampling formula

Rights: Copyright © 2018 Bernoulli Society for Mathematical Statistics and Probability

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Vol.24 • No. 2 • May 2018
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