arXiv subjects

Sibusiso Sibisi

Publications and source records attributed to Sibusiso Sibisi.

3 recordsLinked to original sources

arXiv2026

Representation-free Densities of Ratios and Powers of Stable Variables

We derive representation-free densities of ratios and powers of the positive stable random variable given only its simple Laplace transform. This suffices to obtain Laplace/Stieltjes forward transforms of various {\it r.v.} combinations. We state representation-free densities associated with occupation times (Lamperti~\cite{Lamperti}) and Bessel process excursions (Bertoin~{\it et al.}~\cite{Bertoin}) and their forward transforms. We also readily obtain simple representations of these and other densities using a known infinite series representation of the stable density.

math.PR↗

arXiv2008

Densities, Laplace Transforms and Analytic Number Theory

Li showed that the Riemann Hypothesis is equivalent to the nonnegativity of a certain sequence of numbers. Bombieri and Lagarias gave an arithmetic formula for the number sequence based on the Guinand-Weil explicit formula and showed that Li's criterion is equivalent to Weil's criterion for the Riemann Hypothesis. We provide a derivation of the explicit formula based on Laplace transforms and present an alternative expression for Li's criterion that invites a probabilistic interpretation.

math.NT↗

arXiv2007

Finite Element Model Updating Using Bayesian Approach

This paper compares the Maximum-likelihood method and Bayesian method for finite element model updating. The Maximum-likelihood method was implemented using genetic algorithm while the Bayesian method was implemented using the Markov Chain Monte Carlo. These methods were tested on a simple beam and an unsymmetrical H-shaped structure. The results show that the Bayesian method gave updated finite element models that predicted more accurate modal properties than the updated finite element models obtained through the use of the Maximum-likelihood method. Furthermore, both these methods were found to require the same levels of computational loads.

stat.AP↗