Leif Döring, Lukas Trottner, Alexander R. Watson
Published 2023-08-18Version 1
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.
Splitting and time reversal for Markov additive processes
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