  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.
