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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 ${\tilde{p}}_{t}$ ˜pt := 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...

Exponential deficiency of convolutions of densities∗

Iosif Pinelis (2012)

ESAIM: Probability and Statistics

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 ${\tilde{p}}_{t}$ := 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...

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Eine Momentengleichung bei Exponentialfamilien.

Ergodic properties of locally stationary processes

Euclidean distances on signed measures and application to Berry-Esséen theorems. (Distances euclidiennes sur les mesures signées et application à des théorèmes de Berry-Esséen.)

Existence of a critical point for the infinite divisibility of squares of Gaussian vectors in ℝ 2 with non-zero mean.

Exponential deficiency of convolutions of densities

Exponential deficiency of convolutions of densities∗

Currently displaying 1 – 6 of 6

Existence of a critical point for the infinite divisibility of squares of Gaussian vectors in $ℝ^{2}$ with non-zero mean.