On tails of fixed points of the smoothing transform in the boundary case

DOI10.1016/j.spa.2009.09.005zbMath1183.60031OpenAlexW1991814289MaRDI QIDQ1041057

Dariusz Buraczewski

Publication date: 27 November 2009

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

Full work available at URL: https://doi.org/10.1016/j.spa.2009.09.005

zbMATH Keywords

branching random walkrandom difference equationsmoothing transformdistributional equations

Mathematics Subject Classification ID

Martingales with discrete parameter (60G42) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

Related Items (16)

The fixed points of the multivariate smoothing transform ⋮ Pointwise estimates for first passage times of perpetuity sequences ⋮ Tail asymptotics of maximums on trees in the critical case ⋮ On multidimensional Mandelbrot cascades ⋮ Regular variation of fixed points of the smoothing transform ⋮ Critical Mandelbrot cascades ⋮ Basic properties of critical lognormal multiplicative chaos ⋮ Towards rigorous analysis of the Levitov–Mirlin–Evers recursion ⋮ On the invariant measure of the random difference equation \(X_{n} = a_{n}x_{n - 1} + b_{n}\) in the critical case ⋮ On the law of terminal value of additive martingales in a remarkable branching stable process ⋮ The precise tail behavior of the total progeny of a killed branching random walk ⋮ Linear stochastic equations in the critical case ⋮ Genealogy of the extremal process of the branching random walk ⋮ 1-stable fluctuations in branching Brownian motion at critical temperature. I: The derivative martingale ⋮ On the derivative martingale in a branching random walk ⋮ Anomalous spreading in reducible multitype branching Brownian motion

Cites Work

• On the invariant measure of the random difference equation \(X_{n} = a_{n}x_{n - 1} + b_{n}\) in the critical case
• Implicit renewal theory and tails of solutions of random equations
• Fixed points of the smoothing transform: the boundary case
• Sur une extension de la notion de loi semi-stable. (On an extension of the notion of semi-stable law)
• Random difference equations and renewal theory for products of random matrices
• Seneta-Heyde norming in the branching random walk
• The random difference equation \(X_ n = A_ n X_{n-1} + B_ n\) in the critical case
• On generalized multiplicative cascades
• Asymptotic properties of supercritical age-dependent branching processes and homogeneous branching random walks
• On invariant measures of stochastic recursions in a critical case
• Fixed points of a generalized smoothing transformation and applications to the branching random walk
• Fixed points of the smoothing transformation

This page was built for publication: On tails of fixed points of the smoothing transform in the boundary case