Multifractional Poisson process, multistable subordinator and related limit theorems

TL;DR

This paper introduces a multistable subordinator with a time-varying stability index, leading to the definition of a multifractional Poisson process, and proves convergence of certain random walks to this process.

Contribution

It generalizes stable subordinators to include time-varying stability indices and establishes the convergence of continuous-time random walks to the new multifractional Poisson process.

Findings

Defined a multistable subordinator with variable stability index

Established properties of the multifractional Poisson process

Proved convergence of random walks to the multifractional Poisson process

Abstract

We introduce a multistable subordinator, which generalizes the stable subordinator to the case of time-varying stability index. This enables us to define a multifractional Poisson process. We study properties of these processes and establish the convergence of a continuous-time random walk to the multifractional Poisson process.