On the density of branching Brownian motion

Mehmet Oz

Makale detayları

On the density of branching Brownian motion

Yazarlar:

Mehmet Oz

Yayıncı:

Hacettepe University

Ana Başlıklar:

Statistics

Dergi:

Hacettepe Journal of Mathematics and Statistics Vol.52 Issue 1, pp.229-247

Belge Tipi:

Makale

Yayın Tarihi:

2/2023

Belge Dili:

İngilizce

Document ID (Org No.):

2001283982

pISSN:

2651-477X

Anahtar kelimeler:

Özet:

 We consider a d-dimensional dyadic branching Brownian motion, and study the density of its support in the region where there is typically exponential growth of particles. Using geometric arguments and an extension of a previous result on the probability of absence of branching Brownian motion in linearly moving balls of fixed size, we obtain sharp asymptotic results on the covering radius of the support of branching Brownian motion, which is a measure of its density. As a corollary, we obtain large deviation estimates on the volume of the rt-enlargement of the support of branching Brownian motion when rt decays exponentially in time t. As a by-product, we obtain the lower tail asymptotics for the mass of branching Brownian motion falling in linearly moving balls of exponentially shrinking radius, which is of independent interest.

 We consider a d-dimensional dyadic branching Brownian motion, and study the density of its support in the region where there is typically exponential growth of particles. Using geometric arguments and an extension of a previous result on the probability of absence of branching Brownian motion in linearly moving balls of fixed size, we obtain sharp asymptotic results on the covering radius of the support of branching Brownian motion, which is a measure of its density. As a corollary, we obtain large deviation estimates on the volume of the rt-enlargement of the support of branching Brownian motion when rt decays exponentially in time t. As a by-product, we obtain the lower tail asymptotics for the mass of branching Brownian motion falling in linearly moving balls of exponentially shrinking radius, which is of independent interest.

 We consider a d-dimensional dyadic branching Brownian motion, and study the density of its support in the region where there is typically exponential growth of particles. Using geometric arguments and an extension of a previous result on the probability of absence of branching Brownian motion in linearly moving balls of fixed size, we obtain sharp asymptotic results on the covering radius of the support of branching Brownian motion, which is a measure of its density. As a corollary, we obtain large deviation estimates on the volume of the rt-enlargement of the support of branching Brownian motion when rt decays exponentially in time t. As a by-product, we obtain the lower tail asymptotics for the mass of branching Brownian motion falling in linearly moving balls of exponentially shrinking radius, which is of independent interest.

 We consider a d-dimensional dyadic branching Brownian motion, and study the density of its support in the region where there is typically exponential growth of particles. Using geometric arguments and an extension of a previous result on the probability of absence of branching Brownian motion in linearly moving balls of fixed size, we obtain sharp asymptotic results on the covering radius of the support of branching Brownian motion, which is a measure of its density. As a corollary, we obtain large deviation estimates on the volume of the rt-enlargement of the support of branching Brownian motion when rt decays exponentially in time t. As a by-product, we obtain the lower tail asymptotics for the mass of branching Brownian motion falling in linearly moving balls of exponentially shrinking radius, which is of independent interest.

Makale detayları

On the density of branching Brownian motion

Yazarlar:

Mehmet Oz

Yayıncı:

Hacettepe University

Ana Başlıklar:

Statistics

Dergi:

Hacettepe Journal of Mathematics and Statistics Vol.52 Issue 1, pp.229-247

Belge Tipi:

Makale

Yayın Tarihi:

2/2023

Belge Dili:

İngilizce

Document ID (Org No.):

2001283982

pISSN:

2651-477X

Branching Brownian motion

density

large deviations

neighborhood recurrence

Branching Brownian motion

density

large deviations

neighborhood recurrence

Sayı

Makale detayları

Yazarlar: Mehmet Oz

Yayıncı: Hacettepe University

Ana Başlıklar: Statistics

Dergi: Hacettepe Journal of Mathematics and Statistics Vol.52 Issue 1, pp.229-247

Belge Tipi: Makale

Yayın Tarihi: 2/2023

Belge Dili: İngilizce

Document ID (Org No.): 2001283982

pISSN: 2651-477X

Sayı

Yazarlar:

Mehmet Oz

Yayıncı:

Hacettepe University

Ana Başlıklar:

Statistics

Dergi:

Hacettepe Journal of Mathematics and Statistics Vol.52 Issue 1, pp.229-247

Belge Tipi:

Makale

Yayın Tarihi:

2/2023

Belge Dili:

İngilizce

Document ID (Org No.):

2001283982

pISSN:

2651-477X