Kendall random walk, Williamson transform and the corresponding Wiener-Hopf factorization

TL;DR

This paper explores properties of hitting times and Wiener-Hopf factorization for Kendall random walks, demonstrating that the Williamson transform is an effective tool for analyzing problems related to Kendall generalized convolution.

Contribution

It introduces an analogue of Wiener-Hopf factorization for Kendall random walks and highlights the Williamson transform's utility in this context.

Findings

Properties of hitting times for Kendall random walks

An analogue of Wiener-Hopf factorization established

Williamson transform identified as the optimal analytical tool

Abstract

The paper gives some properties of hitting times and an analogue of the Wiener-Hopf factorization for the Kendall random walk. We show also that the Williamson transform is the best tool for problems connected with the Kendall generalized convolution.