[Autour d'une approche analytique pour les marches à sauts arbitrairement grands dans le quart de plan]
Dans cette note, nous nous intéressons aux marches aléatoires avec sauts arbitrairement grands dans le quart de plan. Nous annonçons le développement, pour cette classe de modèles, de l'approche analytique proposée dans Fayolle et al. (1999) [4], initialement applicable aux marches à petits sauts dans le quart de plan. De nouvelles difficultés théoriques surgissent, qui, pour l'essentiel, sont abordées dans le cadre de la théorie des problèmes aux limites généralisés sur des surfaces de Riemann compactes.
In this note, we consider random walks in the quarter plane with arbitrary big jumps. We announce the extension to that class of models of the analytic approach of [4], initially valid for walks with small steps in the quarter plane. New technical challenges arise, most of them being tackled in the framework of generalized boundary value problems on compact Riemann surfaces.
Accepté le :
Publié le :
Guy Fayolle 1 ; Kilian Raschel 2
@article{CRMATH_2015__353_2_89_0, author = {Guy Fayolle and Kilian Raschel}, title = {About a possible analytic approach for walks in the quarter plane with arbitrary big jumps}, journal = {Comptes Rendus. Math\'ematique}, pages = {89--94}, publisher = {Elsevier}, volume = {353}, number = {2}, year = {2015}, doi = {10.1016/j.crma.2014.11.015}, language = {en}, }
TY - JOUR AU - Guy Fayolle AU - Kilian Raschel TI - About a possible analytic approach for walks in the quarter plane with arbitrary big jumps JO - Comptes Rendus. Mathématique PY - 2015 SP - 89 EP - 94 VL - 353 IS - 2 PB - Elsevier DO - 10.1016/j.crma.2014.11.015 LA - en ID - CRMATH_2015__353_2_89_0 ER -
Guy Fayolle; Kilian Raschel. About a possible analytic approach for walks in the quarter plane with arbitrary big jumps. Comptes Rendus. Mathématique, Volume 353 (2015) no. 2, pp. 89-94. doi : 10.1016/j.crma.2014.11.015. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2014.11.015/
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