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Tail probability and singularity of Laplace-Stieltjes transform of a Pareto type random variable

Kenji Nakagawa (2015)

Applications of Mathematics

We give a sufficient condition for a non-negative random variable X to be of Pareto type by investigating the Laplace-Stieltjes transform of the cumulative distribution function. We focus on the relation between the singularity at the real point of the axis of convergence and the asymptotic decay of the tail probability. For the proof of our theorems, we apply Graham-Vaaler’s complex Tauberian theorem. As an application of our theorems, we consider the asymptotic decay of the stationary distribution...

Tameness on the boundary and Ahlfors' measure conjecture

Jeffrey Brock, Kenneth Bromberg, Richard Evans, Juan Souto (2003)

Publications Mathématiques de l'IHÉS

Let N be a complete hyperbolic 3-manifold that is an algebraic limit of geometrically finite hyperbolic 3-manifolds. We show N is homeomorphic to the interior of a compact 3-manifold, or tame, if one of the following conditions holds: 1. N has non-empty conformal boundary, 2. N is not homotopy equivalent to a compression body, or 3. N is a strong limit of geometrically finite manifolds. The first case proves Ahlfors’ measure conjecture for kleinian groups in the closure of the geometrically finite...

Tchebotaröv’s extremal problem

Promarz Tamrazov (2005)

Open Mathematics

We give the complete solution of the extremal problem posed by N.G. Tchebotaröv in 20th of the last century, and we establish explicit parametric formulae for the extremals.

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