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On the potential theory of one-dimensional subordinate Brownian motions with continuous components. (English) Zbl 1202.60125

Suppose that \(S\) is a subordinator with a nonzero drift and \(W\) is an independent 1-dimensional Brownian motion. The authors study the subordinate Brownian motion \(X\) defined by \(X_t=W(S_t)\). They give sharp bounds for the Green function of the process \(X\) killed upon exiting a bounded open interval and prove a boundary Harnack principle. In the case when \(S\) is a stable subordinator with a positive drift, they also prove sharp bounds for the Green function of \(X\) in \((0,\infty)\), and sharp bounds for the Poisson kernel of \(X\) in a bounded open interval.

MSC:

60J45 Probabilistic potential theory
60G51 Processes with independent increments; Lévy processes
60J25 Continuous-time Markov processes on general state spaces
60J65 Brownian motion
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