Critical branching Brownian motion with killing

DOI10.1214/EJP.V20-4466zbMATH Open1328.60196arXiv1507.02345OpenAlexW2962738184MaRDI QIDQ894181

Bowei Zheng, Steven P. Lalley

Publication date: 27 November 2015

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

Abstract: We obtain sharp asymptotic estimates for hitting probabilities of a critical branching Brownian motion in one dimension with killing at 0 We also obtain sharp asymptotic formulas for the tail probabilities of the number of particles killed at 0. In the special case of double-or-nothing branching, we give exact formulas for both the hitting probabilities, in terms of elliptic functions, and the distribution of the number of killed particles.

Full work available at URL: https://arxiv.org/abs/1507.02345

zbMATH Keywords

tail probabilitiespower lawsingularity analysisWeierstrass elliptic functionbranching Brownian motion

Mathematics Subject Classification ID

Brownian motion (60J65) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Large deviations (60F10) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80) Elliptic functions and integrals (33E05)

Related Items (1)

Conditional limit distributions of critical branching Brownian motions

This page was built for publication: Critical branching Brownian motion with killing

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q894181)