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A Local Limit Theorem for Associated Sequences

open access: yesAnnals of Probability, 1985
A local central limit theorem of the type due to \textit{L. A. Shepp} [Ann. Math. Stat. 35, 419-423 (1964; Zbl 0146.391)] is proved for certain stationary sequences of associated random variables.
exaly   +4 more sources
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Local Limit Theorems for Densities in Orlicz Spaces

Journal of Mathematical Sciences, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
S. G. Bobkov
semanticscholar   +3 more sources

Central limit theorems for local network statistics

Biometrika, 2020
Subgraph counts, in particular the number of occurrences of small shapes such as triangles, characterize properties of random networks. As a result, they have seen wide use as network summary statistics. Subgraphs are typically counted globally, making
P. Maugis
semanticscholar   +1 more source

Local Limit Theorems for Large Deviations

Theory of Probability & Its Applications, 1957
Let $(X_j ),j = 1,2, \cdots $, be a sequence of independent random variables with the distribution functions $V_j (x)$. We assume the existence of ${\bf D}X_j = \sigma _j^2 ,s_n^2 = \sum\nolimits_{j = 1}^n {\sigma _j^2 } ,{\bf E}X_j = 0,j = 1,2, \cdots $. We put \[ Z_n = \sum\limits_{j = 1}^n X_j /s_n .
openaire   +3 more sources

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