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Original scientific paper

Stochastic Models With Mixtures of Tempered Stable Subordinators

Neha Gupta ; Department of Mathematics, Indian Institute of Technology Ropar, Rupnagar, Punjab - 140 001, India
Arun Kumar ; Department of Mathematics, Indian Institute of Technology Ropar, Rupnagar, Punjab - 140 001, India
Nikolai Leonenko ; Cardiff School of Mathematics, Cardiff University, Senghennydd Road, Cardiff, CF24 4AG, UK


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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.

Keywords

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

Hrčak ID:

252602

URI

https://hrcak.srce.hr/252602

Publication date:

10.3.2021.

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