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Unavoidable collections of balls for isotropic Levy processes (CROSBI ID 197126)

Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija

Mimica, Ante ; Vondraček, Zoran Unavoidable collections of balls for isotropic Levy processes // Stochastic processes and their applications, 124 (2014), 3; 1303-1334. doi: 10.1016/j.spa.2013.11.003

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

Povezanost rada

Matematika

Poveznice
Indeksiranost