Fixed points with finite variance of a smoothing transformation.

DOI10.1016/S0304-4149(03)00075-9zbMath1075.60503MaRDI QIDQ2574591

Amke Caliebe, Uwe Roesler

Publication date: 29 November 2005

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

zbMATH Keywords

functional equationsbranching random walksinfinite particle systemsweighted branching processesconvergence of triangular schemesdistributional fixed point equations

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Martingales with discrete parameter (60G42) Central limit and other weak theorems (60F05) Characteristic functions; other transforms (60E10) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

Related Items

The fixed points of the multivariate smoothing transform ⋮ Fixed points of the smoothing transform: two-sided solutions ⋮ Multi-dimensional smoothing transformations: existence, regularity and stability of fixed points ⋮ Heavy tailed solutions of multivariate smoothing transforms ⋮ A weakly 1-stable distribution for the number of random records and cuttings in split trees ⋮ Fixed points of smoothing transformation in random environment ⋮ The functional equation of the smoothing transform ⋮ Elementary fixed points of the BRW smoothing transforms with infinite number of summands ⋮ A survey of max-type recursive distributional equations ⋮ On stochastic recursive equations of sum and max type ⋮ Convergence of complex multiplicative cascades ⋮ Stochastic fixed-point equations ⋮ Dynamics and endogeny for recursive processes on trees ⋮ The Smoothing Transform: A Review of Contraction Results ⋮ Precise Tail Index of Fixed Points of the Two-Sided Smoothing Transform

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