Stochastic models with mixtures of tempered stable subordinators

Abstract

In this article, we introduce mixtures of tempered stable subordinators. These mixtures define a class of subordinators which generalize tempered stable subordinators (TSS). The main properties like the probability density function (pdf), L´evy density, moments, governing Fokker-Planck-Kolmogorov (FPK) type equations and the asymptotic form of potential density are derived. Further, the governing FPK type equation and the 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 the time-changed Poisson process and Brownian motion are also discussed.