On Densities of the Product, Quotient and Power of Independent Subordinators

TL;DR

This paper derives explicit formulas for the densities of the product, quotient, and powers of independent stable subordinators, using Fox's H-function, and extends results to inverse stable subordinators.

Contribution

It provides closed-form density expressions for various operations on stable subordinators and their inverses, advancing analytical understanding of these processes.

Findings

Closed-form densities for product, quotient, and powers of stable subordinators.

Expressions for inverse stable subordinators using Fox's H-function.

Enhanced analytical tools for stable subordinator analysis.

Abstract

We obtain the closed form expressions for the densities of the product, quotient, power and scalar multiple of independent stable subordinators. Similar results for the independent inverse stable subordinators are discussed. This is achieved by expressing the densities of stable and inverse stable subordinators in terms of the Fox's $H$-function.