## Polyhedral approximation of convex sets with an application to large deviation probability theory.(English)Zbl 0835.60021

Authors’ summary: We extend the well-known large deviation upper bound for sums of independent, identically distributed random variables in $$R^d$$ by weakening the requirement that the rate functions have compact level sets (the classical Cramer condition). To do so we establish an apparently new theorem on approximation of closed convex sets by polytopes.

### MSC:

 60F10 Large deviations 52A20 Convex sets in $$n$$ dimensions (including convex hypersurfaces) 52A27 Approximation by convex sets

### Keywords:

large deviation; rate functions; Cramer condition; polytopes
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