Stable-like fluctuations of Biggins' martingales

DOI10.1016/j.spa.2018.11.022zbMath1448.60172arXiv1709.07362OpenAlexW2963150439MaRDI QIDQ2010487

Konrad Kolesko, Matthias Meiners, Aleksander M. Iksanov

Publication date: 27 November 2019

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

Full work available at URL: https://arxiv.org/abs/1709.07362

zbMATH Keywords

martingalebranching random walkstable distributionautoregressive processBiggins' martingale

Mathematics Subject Classification ID

Martingales with discrete parameter (60G42) Central limit and other weak theorems (60F05) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

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Regular variation of fixed points of the smoothing transform ⋮ Berry-Esseen bound and Cramér moderate deviation expansion for a supercritical branching random walk ⋮ Fluctuations of Biggins' martingales at complex parameters ⋮ 1-stable fluctuations in branching Brownian motion at critical temperature. I: The derivative martingale ⋮ Stable central limit theorems for super Ornstein-Uhlenbeck processes ⋮ Convergence of complex martingale for a branching random walk in an independent and identically distributed environment ⋮ Gaussian fluctuations for the directed polymer partition function in dimension \(d\ge 3\) and in the whole \(L^2\)-region ⋮ Gaussian fluctuations and a law of the iterated logarithm for Nerman's martingale in the supercritical general branching process

Cites Work

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• Maximal displacement of critical branching symmetric stable processes
• Branching random walks. École d'Été de Probabilités de Saint-Flour XLII -- 2012
• Modeling teletraffic arrivals by a Poisson cluster process
• Uniform convergence of martingales in the branching random walk
• Parameter estimation for infinite variance fractional ARIMA
• The phase diagram of the complex branching Brownian motion energy model
• Lindley-type equations in the branching random walk
• The supremum of a negative drift random walk with dependent heavy-tailed steps.
• The rate of convergence for weighted branching processes
• Polymers on disordered trees, spin glasses, and traveling waves.
• Point process convergence for branching random walks with regularly varying steps
• Tail behavior of laws stable by random weighted mean
• A central limit theorem and a law of the iterated logarithm for the Biggins martingale of the supercritical branching random walk
• On Interchanging Limits and Integrals
• Максимум критических процессов Гальтона - Ватсона и непрерывные слева случайные блуждания
• On a theorem of bingham and doney
• Asymptotic properties of supercritical branching processes I: The Galton-Watson process
• Asymptotic properties of super-critical branching processes II: Crump-Mode and Jirina processes
• Martingale convergence in the branching random walk
• Asymptotics for Weighted Random Sums
• Some central limit analogues for supercritical Galton-Watson processes