Tail estimates for the Brownian excursion area and other Brownian areas.
We give a sufficient condition for a non-negative random variable 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...
A problem (arisen from applications to networks) is posed about the principal minors of the matrix of transition probabilities of a Markov chain.
A problem (arisen from applications to networks) is posed about the principal minors of the matrix of transition probabilities of a Markov chain.