An application of the Bernoulli part to local limit theorems for moving averages on stationary sequences |
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Authors: | Andr Robert Dabrowski David Mcdonald |
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Institution: | André Robert Dabrowski,David Mcdonald |
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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. |
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Keywords: | Couplings Bernoulli part local limit theorem AMS 1991 subject classifications: Primary 60F99 secondary 60K05 |
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