Large deviations for local mass of branching Brownian motion

Name: Large deviations for local mass of branching Brownian motion
Author: Öz, Mehmet

İsim	Large deviations for local mass of branching Brownian motion
Yazar	Öz, Mehmet
Basım Tarihi:	2020
Basım Yeri	- Instituto Nacional de Matematica Pura e Aplicada
Konu	Branching Brownian motion, Large deviations, Local mass, Local growth
Tür	Süreli Yayın
Dil	İngilizce
Dijital	Evet
Yazma	Hayır
Kütüphane:	Özyeğin Üniversitesi
Demirbaş Numarası	1980-0436
Kayıt Numarası	642d6729-a251-4400-bf72-6aa4bf0407f5
Lokasyon	Natural and Mathematical Sciences
Tarih	2020
Örnek Metin	We study the local mass of a dyadic branching Brownian motion Z evolving in R-d. By 'local mass', we refer to the number of particles of Z that fall inside a ball with fixed radius and time-dependent center, lying in the region where there is typically exponential growth of particles. Using the strong law of large numbers for the local mass of branching Brownian motion and elementary geometric arguments, we find large deviation results giving the asymptotic behavior of the probability that the local mass is atypically small on an exponential scale. As corollaries, we obtain an asymptotic result for the probability of absence of Z in a ball with fixed radius and time-dependent center, and lower tail asymptotics for the local mass in a fixed ball. The proofs are based on a bootstrap argument, which we use to find the lower tail asymptotics for the mass outside a ball with time-dependent radius and fixed center, as well.
DOI	10.30757/ALEA.v17-27
Cilt	17

Kaynağa git Özyeğin Üniversitesi

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Özyeğin Üniversitesi

Kaynağa git

Large deviations for local mass of branching Brownian motion

Yazar Öz, Mehmet

Basım Tarihi 2020

Basım Yeri - Instituto Nacional de Matematica Pura e Aplicada

Konu Branching Brownian motion, Large deviations, Local mass, Local growth

Tür Süreli Yayın

Dil İngilizce

Dijital Evet

Yazma Hayır

Kütüphane Özyeğin Üniversitesi

Demirbaş Numarası 1980-0436

Kayıt Numarası 642d6729-a251-4400-bf72-6aa4bf0407f5

Lokasyon Natural and Mathematical Sciences

Tarih 2020

Örnek Metin We study the local mass of a dyadic branching Brownian motion Z evolving in R-d. By 'local mass', we refer to the number of particles of Z that fall inside a ball with fixed radius and time-dependent center, lying in the region where there is typically exponential growth of particles. Using the strong law of large numbers for the local mass of branching Brownian motion and elementary geometric arguments, we find large deviation results giving the asymptotic behavior of the probability that the local mass is atypically small on an exponential scale. As corollaries, we obtain an asymptotic result for the probability of absence of Z in a ball with fixed radius and time-dependent center, and lower tail asymptotics for the local mass in a fixed ball. The proofs are based on a bootstrap argument, which we use to find the lower tail asymptotics for the mass outside a ball with time-dependent radius and fixed center, as well.

DOI 10.30757/ALEA.v17-27

Cilt 17