Harmonic Functions and Hitting Distributions for Markov Processes

摘要

It is shown that for a Markov process satisfying Hunt's condition A the class of harmonic functions completely determines the family of hitting distributions. Also, the author shows that for certain processes in two dimensions these hitting distributions are completely determined by two suitably chosen independent harmonic functions. This result parallels and extends the well known one dimensional result that hitting distributions are completely determined by one harmonic function. (Author)