TY - JOUR SP - 7699 VL - 377 N1 - This version is the author accepted manuscript. For information on re-use, please refer to the publisher?s terms and conditions. JF - Transactions of the American Mathematical Society A1 - Döring, Leif A1 - Trottner, Lukas A1 - Watson, Alexander R AV - public Y1 - 2024/// TI - Markov additive friendships UR - https://doi.org/10.1090/tran/9266 EP - 7752 ID - discovery10194365 N2 - The Wiener?Hopf factorisation of a Lévy 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 Lévy 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. ER -