Weighted branching and a pathwise renewal equation |
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Authors: | Matthias Meiners |
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Institution: | Institut für Mathematische Statistik, Fachbereich Mathematik, Einsteinstraße 62, D-48149 Münster, Germany |
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Abstract: | This paper is devoted to the study of a pathwise renewal equation for stochastic processes which are functions of a weighted tree defined in a general weighted branching model. Motivated by applications in the analysis of certain stochastic fixed-point equations and in the theory of general (Crump–Mode–Jagers) branching processes, we analyze the solutions to the equation under several conditions, the main result being a characterization of the set of solutions satisfying appropriate integrability conditions. |
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Keywords: | primary 60K05 secondary 60K99 |
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