Variable speed branching Brownian motion 1. Extremal processes in the\n weak correlation regime

2014/03/25 by Anton Bovier, Bovier, Anton, Lisa Hartung +1
Computer Science · Economics, Econometrics and Finance · Mathematics · Medicine · #60G70 #60J80 #82B44 #Bayesian Methods and Mixture Models #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1403.6332

openalex publication_date 2014/03/25 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

We prove the convergence of the extremal processes for variable speed\nbranching Brownian motions where the "speed functions", that describe the\ntime-inhomogeneous variance, lie strictly below their concave hull and satisfy\na certain weak regularity condition. These limiting objects are universal in\nthe sense that they only depend on the slope of the speed function at 0 and\nthe final time t. The proof is based on previous results for two-speed BBM\nobtained in a recent paper of ours and uses Gaussian comparison arguments to\nextend these to the general case.\n

Citations

• Solution of the generalised random energy model
• Constrained Brownian motion: Fluctuations away from circular and parabolic barriers

Related

• The extremal process of two-speed branching Brownian motion
• A simple backward construction of Branching Brownian motion with large displacement and applications
• The extremal process of two-speed branching random walk
• On McKean's martingale in the Bovier-Hartung extremal process
• An ergodic theorem for the extremal process of branching Brownian motion