Publication:
Conditional speed of branching brownian motion, skeleton decomposition and application to random obstacles

Thumbnail Image

Departments

School / College / Institute

Program

KU Authors

Co-Authors

Englander, Janos

Publication Date

Language

Embargo Status

NO

Journal Title

Journal ISSN

Volume Title

Alternative Title

Abstract

We study a branching Brownian motion Z in Rd, among obstacles scattered according to a Poisson random measure with a radially decaying intensity. Obstacles are balls with constant radius and each one works as a trap for the whole motion when hit by a particle. Considering a general offspring distribution, we derive the decay rate of the annealed probability that none of the particles of Z hits a trap, asymptotically in time t. This proves to be a rich problem motivating the proof of a more general result about the speed of branching Brownian motion conditioned on non-extinction. We provide an appropriate "skeleton" decomposition for the underlying Galton-Watson process when supercritical and show that the "doomed" particles do not contribute to the asymptotic decay rate.

Source

Publisher

Institute Henri Poincaré (IHP)

Subject

Mathematics, Statistics and probability

Citation

Has Part

Source

Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques

Book Series Title

Edition

DOI

10.1214/16-AIHP739

item.page.datauri

Link

Rights

Copyrights Note

Endorsement

Review

Supplemented By

Referenced By

0

Views

4

Downloads

View PlumX Details