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An application of the Bernoulli part to local limit theorems for moving averages on stationary sequences
Authors:Andr Robert Dabrowski  David Mcdonald
Institution:André Robert Dabrowski,David Mcdonald
Abstract:We consider partial sums Sn of a general class of stationary sequences of integer-valued random variables, and we provide sufficient conditions for Sn to satisfy a local limit theorem. To prove this result, we introduce a concept called the Bernoulli part. The amount of Bernoulli part in Sn determines the extent to which the density of Sn is relatively flat. If in addition Sn satisfies a global central limit theorem, the local limit theorem follows.
Keywords:Couplings  Bernoulli part  local limit theorem    AMS 1991 subject classifications: Primary 60F99  secondary 60K05  
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