# Stable processes with stationary increments parameterized by metric spaces

## TL;DR

This paper introduces a new family of stable processes indexed by metric spaces with stationary increments, expanding the theory of set-indexed stable processes and providing new representation and limit theorems.

## Contribution

It presents a novel class of stable processes parameterized by metric spaces, including a Chentsov representation and a key result on measure definite kernels.

## Key findings

- Established a new family of stable processes with stationary increments
- Developed a Chentsov representation for these processes
- Proved a limit theorem for set-indexed processes

## Abstract

A new family of stable processes indexed by metric spaces with stationary increments are introduced. They are special cases of a new family of set-indexed stable processes with Chentsov representation. At the heart of the representation, a result on the so-called measure definite kernels is of independent interest. A limit theorem for set-indexed processes is also established.