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Precise Asymptotics in the Law of the Iterated Logarithm of Moving-Average Processes

Acta Mathematica Sinica,English Series 2006年第1期22卷 143-156页

作者： Yun Xia LI Li Xin ZHANG Zhejiang University of Finance and Economics Hangzhou 310012 P. R. China Department of Mathematics Zhejiang University Hangzhou 310028 P. R. China

In this paper, we discuss the moving-average process Xk = ∑i=-∞ ^∞ ai＋kεi, where {εi;-∞ 〈 i 〈 ∞} is a doubly infinite sequence of identically distributed ψ-mixing or negatively associated random variables with mean zeros and finite variances, {ai;-∞ 〈 i 〈 -∞） is an absolutely solutely summable sequence of real numbers.

关键词： Moving-average process ψ-mixing negative association The law of the iterated logarithm

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Spatial point-pattern analysis as a powerful tool in identifying pattern-process relationships in plant ecology: an updated review

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Ecological Processes 2021年第1期10卷 772-794页

作者： Mariem Ben-Said Applied Biology and Pathology Laboratory Department of BiologyFaculty of SciencesAbdelmalek Essaadi UniversityTetouanMorocco

Background:Ecological processes such as seedling establishment,biotic interactions,and mortality can leave footprints on species spatial structure that can be detectable through spatial point-pattern analysis(SPPA).Being widely used in plant ecology,SPPA is increasingly carried out to describe biotic interactions and interpret patternprocess ***,some aspects are still subjected to a non-negligible debate such as required sample size(in terms of the number of points and plot area),the link between the low number of points and frequently observed random(or independent)patterns,and relating patterns to *** this paper,an overview of SPPA is given based on rich and updated literature providing guidance for ecologists(especially beginners)on summary statistics,uni-/bi-/multivariate analysis,unmarked/marked analysis,types of marks,*** ambiguities in SPPA are also ***:SPPA has a long history in plant ecology and is based on a large set of summary statistics aiming to describe species spatial *** mechanisms known to be responsible for species spatial patterns are actually investigated in different biomes and for different *** processes,plant environmental conditions,and human intervention are interrelated and are key drivers of plant spatial *** spite of being not recommended,small sample sizes are more common in *** some areas,periodic forest inventories and permanent plots are scarce although they are key tools for spatial data availability and plant dynamic ***:The spatial position of plants is an interesting source of information that helps to make hypotheses about processes responsible for plant spatial *** the continuous progress of SPPA,some ambiguities require further clarifications.

关键词： Spatial analysis Point-pattern Summary statistics Second-order characteristics Spatial structure Species interactions Competition Facilitation Positive association negative association

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A Berry-Esseen Theorem and a Law of the Iterated Logarithm for Asymptotically negatively Associated Sequences

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Acta Mathematica Sinica,English Series 2007年第1期23卷 127-136页

作者： Jian Feng WANG Li Xin ZHANG Department of Statistics Zhejiang Gongshang University Hangzhou 310035 P R China Department of Mathematics Zhejiang Unversity Hangzhou 310028 P. R. China

negatively associated sequences have been studied extensively in recent years, Asymptotically negative association is a generalization of negative association, In this paper a Berry Esseen theorem and a law of the ite... 详细信息

关键词： Berry-Esseen theorem law of the iterated logarithm negative association asymptotically negative association

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Precise Large Deviation for the Difference of Non-Random Sums of NA Random Variables

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Journal of Mathematical Research with Applications 2016年第6期36卷 732-740页

作者： Zhiqiang HUA Lixin SONG College of Mathematics Inner Mongolia University for the Nationalities School of Mathematical Sciences Dalian University of Technology

In this paper,we study precise large deviation for the non-random difference sum from j=1 to n（t） X-sum from j=1 to n（t） X,where sum from j=1 to n（t） Xis the non-random sum of {X,j≥1} which is a sequence of negatively associated random variables with common distribution F（x）,and sum from j=1 to n（t） Xis the non-random sum of {X,j≥1} which is a sequence of independent and identically distributed random variables,n（t） and n（t） are two positive integer *** some other mild conditions,we establish the following uniformly asymptotic relation lim t→∞ sup x≥r(n（t）)|(P(∑n（t）X-∑n（t）X-(μn（t）-μn（t）>x))/(n（t）F（x）)-1|=0.

关键词： precise large deviation negative association consistently varying tail difference

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