Department of Mathematical Sciences, Michigan Technological University, Houghton, 49931 Michigan, USA. [email protected]
If a probability density p(x) (x ∈ ℝk) is bounded and R(t) := ∫e〈x, tu〉p(x)dx < ∞ for some linear functional u and all t ∈ (0,1), then, for each t ∈ (0,1) and all large enough n, the n-fold convolution of the t-tilted density := e〈x, tu〉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 and their corollaries stated in terms of the absolute integrability of the corresponding characteristic functions are useful for saddle-point approximations.
(Received June 17 2009)
(Revised February 17 2010)
(Online publication July 02 2012)
Mathematics Subject Classification:
∗ Supported by NSF grant DMS-0805946.