Abstract
We provide a sufficient condition for the negative of the infinitesimal generator of a continuous-time finite skip-free Markov chain to have only real and non-negative eigenvalues. The condition includes stochastic monotonicity and certain requirements on the transition rates of the chain. We also give a sample path illustration of Markov chains that satisfy the conditions and its Siegmund dual. We illustrate our result by detailing an example which also reveals that our conditions are not necessary.
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