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Newton potential theory for birth-death processes. (Chinese. English summary) Zbl 0575.60071

In this paper, the author calculates prohibition-potential as moment of some sojourn times, gives the distribution of the first hitting position, consequently obtains Newton potential of processes X. It is shown that in studying Newton potential problems of X one can devote every effort to the investigation of the least chain potential theory. Conclusions about main problems in potential theory can almost all be implanted from ones of Brownian motion after \(\pi\)-symmetry and Z-harmonics are introduced.

MSC:

60J45 Probabilistic potential theory
60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
60J65 Brownian motion
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