Series Representation of Time-Stable Stochastic Processes

TL;DR

This paper explores the series representation of time-stable stochastic processes, providing insights into their structure through LePage series, which enhances understanding of their behavior and properties.

Contribution

It introduces a novel LePage series representation for time-stable processes, advancing theoretical understanding of their structure and distributional properties.

Findings

LePage series representation for time-stable processes established

Enhanced understanding of process behavior through series decomposition

Theoretical framework for analyzing time-stable processes developed

Abstract

A stochastically continuous process $\xi(t)$, $t\geq0$, is said to be time-stable if the sum of $n$ i.i.d. copies of $\xi$ equals in distribution to the time-scaled stochastic process $\xi(nt)$, $t\geq0$. The paper advances the understanding of time-stable processes by means of their LePage series representations.