On \(L^p\)-convergence of the Biggins martingale with complex parameter

DOI10.1016/j.jmaa.2019.07.017zbMath1440.60078arXiv1903.00524OpenAlexW2954986304WikidataQ127552553 ScholiaQ127552553MaRDI QIDQ2320157

Aleksander M. Iksanov, Quan-sheng Liu, Xin Gang Liang

Publication date: 21 August 2019

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1903.00524

zbMATH Keywords

convergence in \(L^p\)complex parametersBiggins' martingales

Mathematics Subject Classification ID

Martingales with discrete parameter (60G42) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80) (L^p)-limit theorems (60F25)

Related Items (5)

Asymptotic expansions in the central limit theorem for a branching Wiener process ⋮ Large and moderate deviations for a -valued branching random walk with a random environment in time ⋮ Fluctuations of Biggins' martingales at complex parameters ⋮ Convergence of complex martingale for a branching random walk in an independent and identically distributed environment ⋮ Convergence of complex martingale for a branching random walk in a time random environment

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A functional central limit theorem for branching random walks, almost sure weak convergence and applications to random trees
• Convergence of complex martingales in the branching random walk: the boundary
• Minimal position and critical martingale convergence in branching random walks, and directed polymers on disordered trees
• A log-type moment result for perpetuities and its application to martingales in supercritical branching random walks
• Uniform convergence of martingales in the branching random walk
• Seneta-Heyde norming in the branching random walk
• On generalized multiplicative cascades
• The phase diagram of the complex branching Brownian motion energy model
• Lindley-type equations in the branching random walk
• Absolute continuity of complex martingales and of solutions to complex smoothing equations
• Fluctuations of Biggins' martingales at complex parameters
• 1-stable fluctuations in branching Brownian motion at critical temperature. I: The derivative martingale
• The Seneta-Heyde scaling for the branching random walk
• Elementary fixed points of the BRW smoothing transforms with infinite number of summands
• Exponential rate of L_p-convergence of intrinsic martingales in supercritical branching random walks
• Asymptotic properties of supercritical branching processes I: The Galton-Watson process
• Martingale convergence in the branching random walk

This page was built for publication: On \(L^p\)-convergence of the Biggins martingale with complex parameter