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Computing the invariant law of a fluid model

In this paper, we discuss a variety of methods for computing the Wiener-Hopf factorization of a finite Markov chain associated to a fluctuating additive functional. The importance of this is that the equilibrium law of a fluid model can be expressed in terms of these Wiener–Hopf factors. The diagonalization methods considered are actually quite efficient, and provide an effective solution to the problem.