α-stable random walk has massive thorns

Alexander Bendikov; Wojciech Cygan

Colloquium Mathematicae, Tome 139 (2015), p. 105-129 / Harvested from The Polish Digital Mathematics Library

Résumé

We introduce and study a class of random walks defined on the integer lattice $ℤ^{d}$ -a discrete space and time counterpart of the symmetric α-stable process in $ℝ^{d}$ . When 0 < α <2 any coordinate axis in $ℤ^{d}$ , d ≥ 3, is a non-massive set whereas any cone is massive. We provide a necessary and sufficient condition for a thorn to be a massive set.

Publié le : 2015-01-01

Zbl 1329.60114

EUDML-ID : urn:eudml:doc:283839

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     author = {Alexander Bendikov and Wojciech Cygan},
     title = {$\alpha$-stable random walk has massive thorns},
     journal = {Colloquium Mathematicae},
     volume = {139},
     year = {2015},
     pages = {105-129},
     zbl = {1329.60114},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm138-1-7}
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Alexander Bendikov; Wojciech Cygan. α-stable random walk has massive thorns. Colloquium Mathematicae, Tome 139 (2015) pp. 105-129. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm138-1-7/