Convergence rates in the implicit renewal theorem on trees

• Autores: Predrag R. Jelenkovic, Mariana Olvera-Cravioto
• Localización: Journal of Applied Probability, ISSN-e 0021-9002, Vol. 50, Nº. 4, 2013, págs. 1077-1088
• Idioma: inglés
• DOI: 10.1017/s0021900200013802
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• Resumen

  • We consider possibly nonlinear distributional fixed-point equations on weighted branching trees, which include the well-known linear branching recursion. In Jelenkovic and Olvera-Cravioto (2012), an implicit renewal theorem was developed that enables the characterization of the power-tail asymptotics of the solutions to many equations that fall into this category. In this paper we complement the analysis in our 2012 paper to provide the corresponding rate of convergence.