Unavoidable collections of balls for isotropic Levy processes (CROSBI ID 197126)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
Podaci o odgovornosti
Mimica, Ante ; Vondraček, Zoran
engleski
Unavoidable collections of balls for isotropic Levy processes
A collection $\{; ; ; ; ; ; \overline{; ; ; ; ; ; B}; ; ; ; ; ; (x_n, r_n)\}; ; ; ; ; ; _{; ; ; ; ; ; n\ge 1}; ; ; ; ; ; $ of pairwise disjoint balls in the Euclidean space $\R^d$ 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 avoidability with respect to unimodal isotropic L\'evy processes satisfying a certain scaling hypothesis. These conditions are expressed in terms of the characteristic exponent of the process, or alternatively, in terms of the corresponding Green function. We also discuss the same problem for a random collection of balls. The results are generalization of several recent results for the case of Brownian motion.
Isotropic Levy process ; Green function ; minimal thinness at infinity
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Podaci o izdanju
124 (3)
2014.
1303-1334
objavljeno
0304-4149
1879-209X
10.1016/j.spa.2013.11.003