A conditional limit theorem for random walks under extreme deviation
Résumé
This paper explores a conditional Gibbs theorem for a random walkinduced by i.i.d. (X₁,..,X_{n}) conditioned on an extreme deviation of its sum (S₁ⁿ=na_{n}) or (S₁ⁿ>na_{n}) where a_{n}→∞. It is proved that when the summands have light tails with some additional regulatity property, then the asymptotic conditional distribution of X₁ can be approximated in variation norm by the tilted distribution at point a_{n} , extending therefore the classical LDP case.
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