The maximum of branching Brownian motion in ℝ^d

2021/04/15 by Yujin H. Kim, Kim, Yujin H., Eyal Lubetzky +3
Mathematics · Decision Sciences · Economics, Econometrics and Finance · #Stochastic processes and statistical mechanics #Probability and Risk Models #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2104.07698

Abstract

We show that in branching Brownian motion (BBM) in ℝ^d, d≥ 2, the law of R_t^*, the maximum distance of a particle from the origin at time t, converges as t→∞ to the law of a randomly shifted Gumbel random variable.

Related

• Branching Brownian motion conditioned on small maximum
• An ergodic theorem for the frontier of branching Brownian motion
• Fine asymptotics for the consistent maximal displacement of branching Brownian motion
• The distance between the two BBM leaders
• Spread rate of branching Brownian motions