Stochastic Models With Mixtures of Tempered Stable Subordinators

Abstract

In this article, we introduce mixtures of tempered stable subordinators (TSS). These mixtures define
a class of subordinators which generalize tempered stable subordinators. The main properties like probability
density function (pdf), L´evy density, moments, governing Fokker-Planck-Kolmogorov (FPK) type equations,
asymptotic form of potential density and asymptotic form of the renewal function for the corresponding inverse
subordinator are discussed. We generalize these results to n-th order mixtures of TSS. The governing fractional
difference and differential equations of time-changed Poisson process and Brownian motion are also discussed.