Stochastic Models With Mixtures of Tempered Stable Subordinators

Neha Gupta, Arun Kumar, Nikolai Leonenko


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.


Tempered stable subordinator; mixtures; Levy density; Fokker-Planck-Kolmogorov equations

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ISSN: 1331-0623 (Print), 1848-8013 (Online)