Markov additive friendships
Probability
2024-10-15 v1
Abstract
The Wiener--Hopf factorisation of a L\'evy or Markov additive process describes the way that it attains new maxima and minima in terms of a pair of so-called ladder height processes. Vigon's theory of friendship for L\'evy processes addresses the inverse problem: when does a process exist which has certain prescribed ladder height processes? We give a complete answer to this problem for Markov additive processes, provide simpler sufficient conditions for constructing processes using friendship, and address in part the question of the uniqueness of the Wiener--Hopf factorisation for Markov additive processes.
Cite
@article{arxiv.2308.09432,
title = {Markov additive friendships},
author = {Leif Döring and Lukas Trottner and Alexander R. Watson},
journal= {arXiv preprint arXiv:2308.09432},
year = {2024}
}