# Asymptotic properties of extremal Markov processes driven by Kendall convolution

## TL;DR

This paper investigates the asymptotic behavior and finite-dimensional distributions of extremal Markov processes driven by Kendall convolution, providing formulas and limit theorems for related random walks and continuous processes.

## Contribution

It introduces a general formula for finite-dimensional distributions of Kendall convolution-driven random walks and establishes new limit theorems for these processes.

## Key findings

- Derived formulas for finite-dimensional distributions
- Proved limit theorems for random walks
- Analyzed asymptotic behavior of extremal Markov processes

## Abstract

This paper is devoted to the analysis of the finite-dimensional distributions and asymptotic behavior of extremal Markov processes connected to the Kendall convolution. In particular, based on its stochastic representation, we provide general formula for finite dimensional distributions of the random walk driven by the Kendall convolution for a large class of step size distributions. Moreover, we prove limit theorems for random walks and connected continuous time stochastic process.