  We consider perturbations of positive recurrent Markov modulated fluid
models. In addition to the infinitesimal generator of the phases, we also
perturb the rate matrix, and analyze the effect of those perturbations on the
matrix of first return probabilities to the initial level. Our main
contribution is the construction of a substitute for the matrix of first return
probabilities, which enables us to analyze the effect of the perturbation under
consideration.
