Continuity of limit random variables in the branching random walk

DOI10.2307/3213141zbMath0425.60069OpenAlexW2317094290MaRDI QIDQ3860603

J. D. Biggins, D. R. Grey

Publication date: 1979

Published in: Journal of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/3213141

zbMATH Keywords

continuityfunctional equationmartingaleabsolute continuitybranching random walkspatially homogeneous branching process

Mathematics Subject Classification ID

Martingales with discrete parameter (60G42) Sums of independent random variables; random walks (60G50) Sample path properties (60G17) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

Related Items

Asymptotic properties of supercritical age-dependent branching processes and homogeneous branching random walks ⋮ Branching processes. II ⋮ Root finding algorithms and persistence of Jordan centrality in growing random trees ⋮ Degree centrality and root finding in growing random networks ⋮ On the law of terminal value of additive martingales in a remarkable branching stable process ⋮ General Edgeworth expansions with applications to profiles of random trees ⋮ Absolute continuity of complex martingales and of solutions to complex smoothing equations ⋮ Asymptotic properties and absolute continuity of laws stable by random weighted mean. ⋮ On conditioning a self-similar growth-fragmentation by its intrinsic area ⋮ Symmetric fixed points of a smoothing transformation ⋮ Minimal position and critical martingale convergence in branching random walks, and directed polymers on disordered trees ⋮ Fixed points with finite variance of a smoothing transformation. ⋮ On weighted branching processes in random environment.