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An application of the Bernoulli part to local limit theorems for moving averages on stationary sequences
Author(s) -
Dabrowski André Robert,
Mcdonald David
Publication year - 1996
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315740
Subject(s) - bernoulli's principle , limit (mathematics) , mathematics , central limit theorem , class (philosophy) , integer (computer science) , law of large numbers , pure mathematics , discrete mathematics , combinatorics , random variable , mathematical analysis , physics , computer science , statistics , artificial intelligence , thermodynamics , programming language
We consider partial sums S n of a general class of stationary sequences of integer‐valued random variables, and we provide sufficient conditions for S n to satisfy a local limit theorem. To prove this result, we introduce a concept called the Bernoulli part. The amount of Bernoulli part in S n determines the extent to which the density of S n is relatively flat. If in addition S n satisfies a global central limit theorem, the local limit theorem follows.