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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...

Technical comment. A problem on Markov chains

Franco Giannessi (2002)

RAIRO - Operations Research - Recherche Opérationnelle

A problem (arisen from applications to networks) is posed about the principal minors of the matrix of transition probabilities of a Markov chain.

Technical comment. A problem on Markov chains

Franco Giannessi (2010)

RAIRO - Operations Research

A problem (arisen from applications to networks) is posed about the principal minors of the matrix of transition probabilities of a Markov chain.

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