# Point processes of non stationary sequences generated by sequential and random dynamical systems

## TL;DR

This paper establishes conditions under which point processes tracking rare events in non-autonomous dynamical systems converge, with applications to sequential and random systems like expanding maps and fibred Lasota-Yorke maps.

## Contribution

It provides general sufficient conditions for convergence of marked point processes in non-autonomous systems, extending the understanding of rare event statistics in these contexts.

## Key findings

- Convergence criteria for point processes in non-stationary systems
- Application to sequential systems with expanding maps
- Application to fibred Lasota-Yorke maps

## Abstract

We give general sufficient conditions to prove the convergence of marked point processes that keep record of the occurrence of rare events and of their impact for non-autonomous dynamical systems. We apply the results to sequential dynamical systems associated to uniformly expanding maps and to random dynamical systems given by fibred Lasota Yorke maps.