Weighted branching and a pathwise renewal equation

Matthias Meiners

Stochastic Processes and their Applications, 2009, vol. 119, issue 8, 2579-2597

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.

Keywords: Weighted; branching; process; Branching; random; walk; General; branching; process; Renewal; equation; Pathwise; renewal; equation; Martingale (search for similar items in EconPapers)
Date: 2009
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