@article{discovery10194365,
         journal = {Transactions of the American Mathematical Society},
           title = {Markov additive friendships},
            year = {2024},
          volume = {377},
            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},
             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}
}