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

Name: Conditional speed of branching Brownian motion, skeleton decomposition and application to random obstacles
Author: Öz, Mehmet, Çağlar, M., Engländer, J.

İsim	Conditional speed of branching Brownian motion, skeleton decomposition and application to random obstacles
Yazar	Öz, Mehmet, Çağlar, M., Engländer, J.
Basım Tarihi:	2017
Basım Yeri	- Institute of Mathematical Statistics
Konu	Branching Brownian motion, Poissonian traps, Random environment, Hard obstacles, Rightmost particle
Tür	Süreli Yayın
Dil	İngilizce
Dijital	Evet
Yazma	Hayır
Kütüphane:	Özyeğin Üniversitesi
Demirbaş Numarası	0246-0203
Kayıt Numarası	292dbc07-137b-4b2c-b6fe-6aae1255abbe
Lokasyon	Natural and Mathematical Sciences
Tarih	2017
Örnek Metin	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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Conditional speed of branching Brownian motion, skeleton decomposition and application to random obstacles

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

Basım Tarihi 2017

Basım Yeri - Institute of Mathematical Statistics

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

Tür Süreli Yayın

Dil İngilizce

Dijital Evet

Yazma Hayır

Kütüphane Özyeğin Üniversitesi

Demirbaş Numarası 0246-0203

Kayıt Numarası 292dbc07-137b-4b2c-b6fe-6aae1255abbe

Lokasyon Natural and Mathematical Sciences

Tarih 2017

Örnek Metin 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