# Particle picture representation of the non-symmetric Rosenblatt process and Hermite processes of any order

## TL;DR

This paper introduces a particle system representation for the non-symmetric Rosenblatt and Hermite processes of any order, showing they can be derived as limits of particle functionals involving stable Lévy motions.

## Contribution

It extends previous work by providing a particle picture for these processes, including non-symmetric cases and arbitrary Hermite orders, using stable Lévy motions.

## Key findings

- Processes are limits of particle functionals involving stable Lévy motions
- Representation applies to non-symmetric Rosenblatt and Hermite processes of any order
- Functional involves k-intersection local time for Hermite processes

## Abstract

We provide a particle picture representation for the non-symmetric Rosenblatt process and for Hermite processes of any order, extending the result of Bojdecki, Gorostiza and Talarczyk in~\cite{FILT}. We show that these processes can be obtained as limits in the sense of finite-dimensional distributions of certain functionals of a system of particles evolving according to symmetric stable L\'{e}vy motions. In the case of $k$-Hermite processes the corresponding functional involves $k$-intersection local time of symmetric stable L\'{e}vy processes