| Issue |
ESAIM: PS
Volume 9, June 2005
|
|
|---|---|---|
| Page(s) | 116 - 142 | |
| DOI | https://doi.org/10.1051/ps:2005006 | |
| Published online | 15 November 2005 | |
Large deviations for independent random variables – Application to Erdös-Renyi's functional law of large numbers
CNRS, École Nationale Supérieure des Télécommunications, 46 rue Barrault 75634 Paris Cedex 13, France; najim@tsi.enst.fr
Received:
13
November
2003
A Large Deviation Principle (LDP) is proved for the family 
where the deterministic probability measure
converges weakly to a
probability measure R and 
are 
-valued independent
random variables whose distribution depends on 
and satisfies the
following exponential moments condition:
In this context, the identification of the rate function is non-trivial due to the absence of equidistribution. We rely on fine convex analysis to address this issue. Among the applications of this result, we extend Erdös and Rényi's functional law of large numbers.
Mathematics Subject Classification: 46E30 / 60F10 / 60G57
Key words: Large deviations / epigraphical convergence / Erdös-Rényi's law of large numbers.
© EDP Sciences, SMAI, 2005
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