Fixed points of inhomogeneous smoothing transforms

DOI10.1080/10236198.2011.589514zbMath1275.60019arXiv1007.4509OpenAlexW3105962955MaRDI QIDQ2902283

Gerold Alsmeyer, Matthias Meiners

Publication date: 17 August 2012

Published in: Journal of Difference Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1007.4509

zbMATH Keywords

Laplace transformbranching random walkmultiplicative martingalesstochastic fixed-point equation

Mathematics Subject Classification ID

Characteristic functions; other transforms (60E10) Probability distributions: general theory (60E05) Functional equations for real functions (39B22) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

Related Items (20)

Solutions to complex smoothing equations ⋮ Implicit Renewal Theory and Power Tails on Trees ⋮ The fixed points of the multivariate smoothing transform ⋮ The Weighted Branching Process ⋮ Tail asymptotics of maximums on trees in the critical case ⋮ Hausdorff and packing spectra, large deviations, and free energy for branching random walks in \({\mathbb{R}^d}\) ⋮ Fixed points of the smoothing transform: two-sided solutions ⋮ Stochastic recursions on directed random graphs ⋮ Solutions of kinetic-type equations with perturbed collisions ⋮ Heavy tailed solutions of multivariate smoothing transforms ⋮ Maximums on trees ⋮ PageRank's behavior under degree correlations ⋮ The functional equation of the smoothing transform ⋮ Linear stochastic equations in the critical case ⋮ Stochastic fixed-point equations ⋮ Convergence of the population dynamics algorithm in the Wasserstein metric ⋮ Stationary Waiting Time in Parallel Queues with Synchronization ⋮ The Smoothing Transform: A Review of Contraction Results ⋮ Precise Tail Index of Fixed Points of the Two-Sided Smoothing Transform ⋮ Precise tail asymptotics of fixed points of the smoothing transform with general weights

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• Fixed points of a generalized smoothing transformation and applications to the branching random walk
• Fixed points of the smoothing transformation

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