Random walks in ( ℤ + ) 2 with non-zero drift absorbed at the axes

Irina Kurkova; Kilian Raschel

Bulletin de la Société Mathématique de France (2011)

  • Volume: 139, Issue: 3, page 341-387
  • ISSN: 0037-9484

Abstract

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Spatially homogeneous random walks in ( ℤ + ) 2 with non-zero jump probabilities at distance at most 1 , with non-zero drift in the interior of the quadrant and absorbed when reaching the axes are studied. Absorption probabilities generating functions are obtained and the asymptotic of absorption probabilities along the axes is made explicit. The asymptotic of the Green functions is computed along all different infinite paths of states, in particular along those approaching the axes.

How to cite

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Kurkova, Irina, and Raschel, Kilian. "Random walks in $(\mathbb {Z}_{+})^{2}$ with non-zero drift absorbed at the axes." Bulletin de la Société Mathématique de France 139.3 (2011): 341-387. <http://eudml.org/doc/272541>.

@article{Kurkova2011,
abstract = {Spatially homogeneous random walks in $(\mathbb \{Z\}_\{+\})^\{2\}$ with non-zero jump probabilities at distance at most $1$, with non-zero drift in the interior of the quadrant and absorbed when reaching the axes are studied. Absorption probabilities generating functions are obtained and the asymptotic of absorption probabilities along the axes is made explicit. The asymptotic of the Green functions is computed along all different infinite paths of states, in particular along those approaching the axes.},
author = {Kurkova, Irina, Raschel, Kilian},
journal = {Bulletin de la Société Mathématique de France},
keywords = {random walk; Green functions; absorption probabilities; singularities of complex functions; holomorphic continuation; steepest descent method},
language = {eng},
number = {3},
pages = {341-387},
publisher = {Société mathématique de France},
title = {Random walks in $(\mathbb \{Z\}_\{+\})^\{2\}$ with non-zero drift absorbed at the axes},
url = {http://eudml.org/doc/272541},
volume = {139},
year = {2011},
}

TY - JOUR
AU - Kurkova, Irina
AU - Raschel, Kilian
TI - Random walks in $(\mathbb {Z}_{+})^{2}$ with non-zero drift absorbed at the axes
JO - Bulletin de la Société Mathématique de France
PY - 2011
PB - Société mathématique de France
VL - 139
IS - 3
SP - 341
EP - 387
AB - Spatially homogeneous random walks in $(\mathbb {Z}_{+})^{2}$ with non-zero jump probabilities at distance at most $1$, with non-zero drift in the interior of the quadrant and absorbed when reaching the axes are studied. Absorption probabilities generating functions are obtained and the asymptotic of absorption probabilities along the axes is made explicit. The asymptotic of the Green functions is computed along all different infinite paths of states, in particular along those approaching the axes.
LA - eng
KW - random walk; Green functions; absorption probabilities; singularities of complex functions; holomorphic continuation; steepest descent method
UR - http://eudml.org/doc/272541
ER -

References

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