A central limit theorem and law of the iterated logarithm for a random field with exponential decay of correlations

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	A central limit theorem and law of the iterated logarithm for a random field with exponential decay of correlations
	Schmuland, B ; Sun, W
	2004-02-01
发表期刊	CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES
ISSN	0008-414X
卷号	56 期号:1 页码:209-224
摘要	In [6], Walter Philipp wrote that "...the law of the iterated logarithm holds for any process for which the Borel-Cantelli Lemma, the central limit theorem with a reasonably good remainder and a certain maximal inequality are valid". Many authors [1], [2], [4], [5], [9] have followed this plan in proving the law of the iterated logarithm for sequences (or fields) of dependent random variables. We carry on this tradition by proving the law of the iterated logarithm for a random field whose correlations satisfy an exponential decay condition like the one obtained by Spohn [8] for certain Gibbs measures. These do not fall into the phi-mixing or strong mixing cases established in the literature, but are needed for our investigations [7] into diffusions on configuration space. The proofs are all obtained by patching together standard results from [5], [9] while keeping a careful eye on the correlations.
关键词	law of the iterated logarithm
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000188711600010
出版者	CANADIAN MATHEMATICAL SOC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/19412
专题	中国科学院数学与系统科学研究院
通讯作者	Schmuland, B
作者单位	1.Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada 2.Chinese Acad Sci, Inst Appl Math, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Schmuland, B,Sun, W. A central limit theorem and law of the iterated logarithm for a random field with exponential decay of correlations[J]. CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES,2004,56(1):209-224.
APA	Schmuland, B,&Sun, W.(2004).A central limit theorem and law of the iterated logarithm for a random field with exponential decay of correlations.CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES,56(1),209-224.
MLA	Schmuland, B,et al."A central limit theorem and law of the iterated logarithm for a random field with exponential decay of correlations".CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES 56.1(2004):209-224.