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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
Source PublicationCANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES
ISSN0008-414X
Volume56Issue:1Pages:209-224
AbstractIn [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.
Keywordlaw of the iterated logarithm
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000188711600010
PublisherCANADIAN MATHEMATICAL SOC
Citation statistics
Cited Times:2[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/19412
Collection中国科学院数学与系统科学研究院
Affiliation1.Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada
2.Chinese Acad Sci, Inst Appl Math, Beijing 100080, Peoples R China
Recommended Citation
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.
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