α-stable random walk has massive thorns

Alexander Bendikov, and Wojciech Cygan. "α-stable random walk has massive thorns." Colloquium Mathematicae 138.1 (2015): 105-129. <http://eudml.org/doc/283839>.

@article{AlexanderBendikov2015,
abstract = {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.},
author = {Alexander Bendikov, Wojciech Cygan},
journal = {Colloquium Mathematicae},
keywords = {-stable random walk; recurrent set; Green function; capacity; regular variation; Lévy process; subordination},
language = {eng},
number = {1},
pages = {105-129},
title = {α-stable random walk has massive thorns},
url = {http://eudml.org/doc/283839},
volume = {138},
year = {2015},
}

TY - JOUR
AU - Alexander Bendikov
AU - Wojciech Cygan
TI - α-stable random walk has massive thorns
JO - Colloquium Mathematicae
PY - 2015
VL - 138
IS - 1
SP - 105
EP - 129
AB - 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.
LA - eng
KW - -stable random walk; recurrent set; Green function; capacity; regular variation; Lévy process; subordination
UR - http://eudml.org/doc/283839
ER -