Lower deviation and moderate deviation probabilities for maximum of a branching random walk
X Chen, H He - 2020 - projecteuclid.org
Given a supercritical branching random walk on R started from the origin, let M_n be the
maximal position of individuals at the n th generation. Under some mild conditions, it is …
maximal position of individuals at the n th generation. Under some mild conditions, it is …
Large deviations for local mass of branching Brownian motion
M Öz - arXiv preprint arXiv:1811.09037, 2018 - arxiv.org
We study the local mass of a dyadic branching Brownian motion $ Z $ evolving in $\mathbb
{R}^ d $. By'local mass,'we refer to the number of particles of $ Z $ that fall inside a ball with …
{R}^ d $. By'local mass,'we refer to the number of particles of $ Z $ that fall inside a ball with …
On the density of branching Brownian motion
M Oz - Hacettepe Journal of Mathematics and Statistics, 2023 - dergipark.org.tr
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 …
support in the region where there is typically exponential growth of particles. Using …
Extremes of log-correlated random fields and the Riemann zeta function, and some asymptotic results for various estimators in statistics
F Ouimet - 2019 - papyrus.bib.umontreal.ca
In this thesis, we study the extreme values of certain log-correlated random fields that are
Gaussian (the scale-inhomogeneous Gaussian free field and the time-inhomogeneous …
Gaussian (the scale-inhomogeneous Gaussian free field and the time-inhomogeneous …
Lower deviation probabilities for level sets of the branching random walk
S Zhang - Journal of Theoretical Probability, 2023 - Springer
Given a supercritical branching random walk {Z n} n≥ 0 on R, let Z n (A) be the number of
particles located in a set A⊂ R at generation n. It is known from Biggins (J Appl Probab 14 …
particles located in a set A⊂ R at generation n. It is known from Biggins (J Appl Probab 14 …
Branching brownian motion conditioned on large level sets
X Chen, H Ma - arXiv preprint arXiv:2409.16104, 2024 - arxiv.org
We study the precise large deviation probabilities for the sizes of intermediate level sets in
branching Brownian motion (BBM). Our conclusions improve on a result of A\"{i} dekon, Hu …
branching Brownian motion (BBM). Our conclusions improve on a result of A\"{i} dekon, Hu …
Large deviations of extremes in branching random walk with regularly varying displacements
A Bhattacharya - arXiv preprint arXiv:1802.05938, 2018 - arxiv.org
In this article, we consider a branching random walk on the real-line where displacements
coming from the same parent have jointly regularly varying tails. The genealogical structure …
coming from the same parent have jointly regularly varying tails. The genealogical structure …
Upper deviation probabilities for level sets of a supercritical branching random walk
S Zhang, L Luo - arXiv preprint arXiv:2402.03872, 2024 - arxiv.org
Given a supercritical branching random walk $\{Z_n\} _ {n\geq 0} $ on $\mathbb {R} $, let $
Z_n ([y,\infty)) $ be the number of particles located in $[y,\infty)\subset\mathbb {R} $ at …
Z_n ([y,\infty)) $ be the number of particles located in $[y,\infty)\subset\mathbb {R} $ at …
On large-deviation probabilities for the empirical distribution of branching random walks with heavy tails
S Zhang - Journal of Applied Probability, 2022 - cambridge.org
Given a branching random walk on, let be the number of particles located in interval A at
generation n. It is well known that under some mild conditions, converges almost surely to …
generation n. It is well known that under some mild conditions, converges almost surely to …
Moderate deviation probabilities for empirical distribution of the branching random walk
Y Jiang, S Zhang - Journal of Mathematical Analysis and Applications, 2023 - Elsevier
Given a super-critical branching random walk {Z n} n≥ 0 on R, let Z n (A) be the number of
particles located in some Borel set A⊂ R at generation n. Under some mild conditions, it's …
particles located in some Borel set A⊂ R at generation n. Under some mild conditions, it's …