eprintid: 10194365 rev_number: 14 eprint_status: archive userid: 699 dir: disk0/10/19/43/65 datestamp: 2024-07-10 07:19:03 lastmod: 2024-12-02 15:29:44 status_changed: 2024-07-10 07:19:03 type: article metadata_visibility: show sword_depositor: 699 creators_name: Döring, Leif creators_name: Trottner, Lukas creators_name: Watson, Alexander R title: Markov additive friendships ispublished: pub divisions: UCL divisions: B04 divisions: C06 divisions: F61 note: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. abstract: 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. date: 2024 date_type: published official_url: https://doi.org/10.1090/tran/9266 oa_status: green full_text_type: other language: eng primo: open primo_central: open_green verified: verified_manual elements_id: 2293188 doi: 10.1090/tran/9266 lyricists_name: Watson, Alexander lyricists_id: AWATS72 actors_name: Watson, Alexander actors_id: AWATS72 actors_role: owner full_text_status: public publication: Transactions of the American Mathematical Society volume: 377 pagerange: 7699-7752 citation: Döring, Leif; Trottner, Lukas; Watson, Alexander R; (2024) Markov additive friendships. Transactions of the American Mathematical Society , 377 pp. 7699-7752. 10.1090/tran/9266 <https://doi.org/10.1090/tran%2F9266>. Green open access document_url: https://discovery.ucl.ac.uk/id/eprint/10194365/1/map_friends_rev.pdf