Fluctuations of Biggins' martingales at complex parameters

DOI10.1214/20-AIHP1046zbMath1479.60177arXiv1806.09943OpenAlexW3094488527MaRDI QIDQ2028944

Aleksander M. Iksanov, Konrad Kolesko, Matthias Meiners

Publication date: 3 June 2021

Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1806.09943

zbMATH Keywords

rate of convergencecentral limit theorempoint processesstable processesbranching random walkminimal positioncomplex martingalesBiggins' martingale

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Strong limit theorems (60F15) Stable stochastic processes (60G52) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items (6)

Large and moderate deviations for a -valued branching random walk with a random environment in time ⋮ The phase diagram of the complex branching Brownian motion energy model ⋮ On the derivative martingale in a branching random walk ⋮ Self-similar solutions to kinetic-type evolution equations: beyond the boundary case ⋮ On \(L^p\)-convergence of the Biggins martingale with complex parameter ⋮ Gaussian fluctuations and a law of the iterated logarithm for Nerman's martingale in the supercritical general branching process

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