In this paper, we obtain sample path and scalar large deviation principles for the product of sums of positive random variables. We study the case when the positive random variables are independent and identically distributed and bounded away from zero or the left tail decays to zero sufficiently fast. The explicit formula for the rate function of a scalar large deviation principle is given in the case when random variables are exponentially distributed.
Bibliographical noteFunding Information:
The author thanks an anonymous referee for the helpful suggestions. The author is supported by NSF Grant DMS-0904701 , DARPA Grant and MacCracken Fellowship at New York University .
- Large deviations
- Product of sums of random variables
- Sample paths