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Let {Xti t O} be a Markov process in Rl, and break up the path X t into (random) component pieces consisting of the zero set ({ tlX = O}) and t the "excursions away from 0," that is pieces of path X.: T::5 s::5 t, with Xr- = X = 0, but X. 1= 0 for T

This advanced text explores the relationship between Markov processes and potential theory, in addition to aspects of the theory of additive functionals. Geared toward graduate students, "Markov Processes and Potential Theory" assumes a familiarity with general measure theory, while offering a nearly self-contained treatment.
Topics include Markov processes, excessive functions, multiplicative functionals and subprocesses, and additive functionals and their potentials. A concluding chapter examines dual processes and potential theory. Exercises appear throughout the text, and a selection...