[Marches aléatoires dans
Dans cet article, nous étudions les marches aléatoires du quart de plan ayant des sauts à distance au plus un, avec un drift non nul à l'intérieur et absorbées au bord. Nous obtenons de façon explicite les séries génératrices des probabilités d'absorption au bord, puis leur asymptotique lorsque le site d'absorption tend vers l'infini. Nous calculons également l'asymptotique des fonctions de Green le long de toutes les trajectoires, en particulier selon celles tangentes aux axes.
Spatially homogeneous random walks in
Keywords: random walk, Green functions, absorption probabilities, singularities of complex functions, holomorphic continuation, steepest descent method
Mot clés : marche aléatoire, fonctions de Green, probabilités d'absorption, singularités de fonctions complexes, prolongement analytique, méthode de la plus grande descente
@article{BSMF_2011__139_3_341_0, author = {Kurkova, Irina and Raschel, Kilian}, title = {Random walks in $(\mathbb {Z}_{+})^{2}$ with non-zero drift absorbed at the axes}, journal = {Bulletin de la Soci\'et\'e Math\'ematique de France}, pages = {341--387}, publisher = {Soci\'et\'e math\'ematique de France}, volume = {139}, number = {3}, year = {2011}, doi = {10.24033/bsmf.2611}, mrnumber = {2869310}, zbl = {1243.60042}, language = {en}, url = {http://www.numdam.org/articles/10.24033/bsmf.2611/} }
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 SP - 341 EP - 387 VL - 139 IS - 3 PB - Société mathématique de France UR - http://www.numdam.org/articles/10.24033/bsmf.2611/ DO - 10.24033/bsmf.2611 LA - en ID - BSMF_2011__139_3_341_0 ER -
%0 Journal Article %A Kurkova, Irina %A Raschel, Kilian %T Random walks in $(\mathbb {Z}_{+})^{2}$ with non-zero drift absorbed at the axes %J Bulletin de la Société Mathématique de France %D 2011 %P 341-387 %V 139 %N 3 %I Société mathématique de France %U http://www.numdam.org/articles/10.24033/bsmf.2611/ %R 10.24033/bsmf.2611 %G en %F BSMF_2011__139_3_341_0
Kurkova, Irina; Raschel, Kilian. Random walks in $(\mathbb {Z}_{+})^{2}$ with non-zero drift absorbed at the axes. Bulletin de la Société Mathématique de France, Tome 139 (2011) no. 3, pp. 341-387. doi : 10.24033/bsmf.2611. http://www.numdam.org/articles/10.24033/bsmf.2611/
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