A collection {B¯(xn,rn)}n⩾1 of pairwise disjoint balls in the Euclidean space Rd is said to be avoidable with respect to a transient process X if the process with positive probability escapes to infinity without hitting any ball. In this paper we study sufficient and necessary conditions for...

In this paper, we consider a large class of subordinate Brownian motions X via subordinators with Laplace exponents which are complete Bernstein functions satisfying some mild scaling conditions at zero and at infinity. We first discuss how such conditions govern the behavior of the subordinator...

In this paper we study a subordinate Brownian motion with a Gaussian component and a rather general discontinuous part. The assumption on the subordinator is that its Laplace exponent is a complete Bernstein function with a Lévy density satisfying a certain growth condition near zero. The main...

We establish a boundary Harnack principle for a large class of subordinate Brownian motions, including mixtures of symmetric stable processes, in [kappa]-fat open sets (disconnected analogue of John domains). As an application of the boundary Harnack principle, we identify the Martin boundary...

Let [psi] be the characteristic exponent of a symmetric Lévy process X. The functionappears in various studies on the local time of X. We study monotonicity properties of the function h. In case when X is a subordinate Brownian motion, we show that is a Bernstein function.