engleski

On the potential theory of one-dimensional subordinate Brownian motions with continuous components

Suppose that $S$ is a subordinator with a nonzero drift and $W$ is an independent 1-dimensional Brownian motion. We study the subordinate Brownian motion $X$ defined by $X_t=W(S_t)$. We 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, we 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.

subordinator ; subordinate Brownian motion ; Green function ; Poisson kernel ; boundary Harnack principle

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