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Conditional speed of branching Brownian motion, skeleton decomposition and application to random obstacles

Title	Conditional speed of branching Brownian motion, skeleton decomposition and application to random obstacles
Author	Öz, Mehmet, Çağlar, M., Engländer, J.
Publication Date:	2017
Publication Place	- Institute of Mathematical Statistics
Subject	Branching Brownian motion, Poissonian traps, Random environment, Hard obstacles, Rightmost particle
Type	Periodical
Language	English
Digital	Yes
Manuscript	No
Library:	Özyeğin University
Library Asset ID	0246-0203
Record ID	292dbc07-137b-4b2c-b6fe-6aae1255abbe
Library Location	Natural and Mathematical Sciences
Date	2017
Sample Text	We study a branching Brownian motion ZZ in RdRd, 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 ZZ hits a trap, asymptotically in time tt. 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.
DOI	10.1214/16-AIHP739

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Özyeğin University

Conditional speed of branching Brownian motion, skeleton decomposition and application to random obstacles

Author Öz, Mehmet, Çağlar, M., Engländer, J.

Publication Date 2017

Publication Place - Institute of Mathematical Statistics

Subject Branching Brownian motion, Poissonian traps, Random environment, Hard obstacles, Rightmost particle

Type Periodical

Language English

Digital Yes

Manuscript No

Library Özyeğin University

Library Asset ID 0246-0203

Record ID 292dbc07-137b-4b2c-b6fe-6aae1255abbe

Library Location Natural and Mathematical Sciences

Date 2017

Sample Text We study a branching Brownian motion ZZ in RdRd, 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 ZZ hits a trap, asymptotically in time tt. 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.

DOI 10.1214/16-AIHP739