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Reports (Research Report) Year : 1995

Large deviation probability and local density of sets

Philippe Barbe
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Abstract

Let $X_1, X_2, \ldots , X_n$ be $n$ independent identically distributed real random variables and $S_n := \displaystyle \sum^n_{i=1} X_i$. We obtain precise asymptotics for $P(S_n \in n A)$ for rather arbitrary Borel sets $A$, in terms of the density of the dominating points in $A$. Our result extends classical theorems in the field of large deviations for independent samples. We also obtain asymptotics for $P(S_n \in \gamma_n A)$, with $\gamma_n/n \rightarrow \infty$.

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Other [cs.OH]
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Dates and versions

inria-00074057 , version 1 (24-05-2006)

Identifiers

  • HAL Id : inria-00074057 , version 1

Cite

Philippe Barbe, Michel Broniatowski. Large deviation probability and local density of sets. [Research Report] RR-2630, INRIA. 1995. ⟨inria-00074057⟩
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