Sharp bounds for Green functions and jumping functions of subordinate killed Brownian motions in bounded domains.
On the relationship between subordinate killed and killed subordinate processes.
The excessive domination principle is equivalent to the weak sector condition
On suprema of Lévy processes and application in risk theory
Let =− where is a general one-dimensional Lévy process and an independent subordinator. Consider the times when a new supremum of is reached by a jump of the subordinator . We give a necessary and sufficient condition in order for such times to be discrete. When this is the case and drifts to −∞, we decompose the absolute supremum of at these times, and derive a Pollaczek–Hinchin-type formula for the distribution function of the supremum.
Minimal thinness for subordinate Brownian motion in half-space
We study minimal thinness in the half-space for a large class of subordinate Brownian motions. We show that the same test for the minimal thinness of a subset of below the graph of a nonnegative Lipschitz function is valid for all processes in the considered class. In the classical case of Brownian motion this test was proved by Burdzy.
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