Exponential deficiency of convolutions of densities

Details Exponential deficiency of convolutions of densities Exponential deficiency of convolutions of densities

2009-05-18

arxiv.org/abs/0905.2944v1

Mathematics

Probability

12 pages, one figure

Scientific paper

If a probability density p(\x) (\x\in\R^k) is bounded and R(t) := \int \exp(t\ell(\x)) \d\x < \infty for some linear functional \ell and all t\in(0,1), then, for each t\in(0,1) and all large enough n, the n-fold convolution of the t-tilted density p_t(\x) := \exp(t\ell(\x)) p(\x)/R(t) is bounded. This is a corollary of a general, "non-i.i.d." result, which is also shown to enjoy a certain optimality property. Such results are useful for saddle-point approximations.

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