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For a skip-free Markov process on non-negative integers with generator matrixQ, we evaluate the joint Laplace transform of the occupation times beforehitting the state n (starting at 0). This Laplace transform has a verystraightforward and familiar expression. We investigate the properties of thisLaplace transform, especially the conditions under which the occupation timesform a Markov chain.

The joint distribution of occupation times of skip-free Markov processes and a class of multivariate exponential distributions