Construction of Right Processes from Hitting Distributions
Let K be the one-point compactification of a locally compact second countable Hausdorff space and Δ ∈ K be the point at infinity. We are concerned with the problem of constructing Markov processes on K with Δ as the adjoined death point, from given hitting distributions. The most general Markov processes for the consideration of this problem (and indeed for the study of probabilistic potential theory) are those now known as right processes on a space K as above. (See .) It is well known that such a process is determined, up to a (random) time change, by its hitting distributions of compact sets of the state space. Our problem is therefore to construct a right process on K with prescribed hitting distributions HD(x,·) for all compact D ⊂ K and x ∈ K.
KeywordsMarkov Process Markov Property Uniform Integrability Strong Markov Property Hold Point
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