Entrance-Exit Distributions for Markov Additive Processes.

摘要

Let X be a standard Markov process, and let S be a perfectly additive increasing process with conditionally independent increments given the paths of X. Then, (X,S) is a Markov additive process. Let C be the random time change associated with S, and put Z(t)(-) = X(C(t)-), Z(t)(+) = X(C(t)), R(t)(-) = t-S(C(t)-), R(t)(+) = S(C(t))-t. When the state space of X if finite, Getoor has recently obtained the joint distribution of these variables in terms of a triple Laplace transform. Here, the same is obtained explicitly by using renewal theoretic arguments along with the results on Levy systems of (X,S) given in Cinlar. These results are useful in reliability theory and in the boundary theory of Markov processes. (Author)