Branching Brownian motion with an inhomogeneous breeding potential

DOI10.1214/08-AIHP300zbMath1183.60029MaRDI QIDQ731736

Simon C. Harris, John W. Harris

Publication date: 8 October 2009

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

Full work available at URL: https://eudml.org/doc/78044

zbMATH Keywords

asymptoticsbranching Brownian motionadditive martingalespopulation explosionsright-most particlespine constructions

Mathematics Subject Classification ID

Brownian motion (60J65) Applications of branching processes (60J85)

Related Items (11)

Spread rate of branching Brownian motions ⋮ Branching Random Walk in an Inhomogeneous Breeding Potential ⋮ Unnamed Item ⋮ The spread of a catalytic branching random walk ⋮ Superdiffusions with super-exponential growth: construction, mass and spread ⋮ A Gaussian particle distribution for branching Brownian motion with an inhomogeneous branching rate ⋮ Branching Brownian motion with catalytic branching at the origin ⋮ Growth rates of the population in a branching Brownian motion with an inhomogeneous breeding potential ⋮ The almost-sure population growth rate in branching Brownian motion with a quadratic breeding potential ⋮ Branching Brownian motion with spatially homogeneous and point-catalytic branching ⋮ A Spine Approach to Branching Diffusions with Applications to L p -Convergence of Martingales

Cites Work

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• KPP equation and supercritical branching Brownian motion in the subcritical speed area. Application to spatial trees
• Travelling wave solutions to the K-P-P equation: alternatives to Simon Harris' probabilistic analysis.
• Change of measures for Markov chains and the \(L\log L\) theorem for branching processes
• Local extinction versus local exponential growth for spatial branching processes.
• Conceptual proofs of \(L\log L\) criteria for mean behavior of branching processes
• A Spine Approach to Branching Diffusions with Applications to L p -Convergence of Martingales
• Convergence of solutions of the Kolmogorov equation to travelling waves
• Maximal displacement of branching brownian motion

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