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Potential theory for a family of several Markov processes. (English) Zbl 0625.60086
This paper develops some potential theory for multiparameter processes \(X(t)=(X^ 1(t^ 1),...,X^ k(t^ k))\), where the \(X^ i\) are independent Markov processes. Among the results are a section-type theorem and a “strong Markov” property, where stopping times are replaced by optional random measures, and the construction of a fine topology for X. Two notions of “small” sets are discussed for the cases \(X^ i\) symmetric and \(X^ i\) Lévy.
The last section contains applications to the problem of multiple points for Lévy processes, including the proof of a conjecture due to Hendricks and Taylor for symmetric Lévy processes [W. J. Hendricks, Z. Wahrscheinlichkeitstheor. Verw. Geb. 49, 13-21 (1979; Zbl 0388.60045)].
Reviewer: J.Mitro

60J45 Probabilistic potential theory
60J25 Continuous-time Markov processes on general state spaces
60J99 Markov processes
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