@article{discovery10194365, note = {This version is the author accepted manuscript. For information on re-use, please refer to the publisher's terms and conditions.}, pages = {7699--7752}, year = {2024}, volume = {377}, title = {Markov additive friendships}, journal = {Transactions of the American Mathematical Society}, url = {https://doi.org/10.1090/tran/9266}, abstract = {The Wiener-Hopf factorisation of a L{\'e}vy or Markov additive process describes the way that it attains new extrema in terms of a pair of so-called ladder height processes. Vigon's theory of friendship for L{\'e}vy 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.}, author = {D{\"o}ring, Leif and Trottner, Lukas and Watson, Alexander R} }