Year: 2020
Type: article
Abstract: The branching Brownian sausage in $\mathbb{R} ^{d}$ was defined in [4] similarly to the classical Wiener sausage, as the random subset of $\mathbb{R} ^{d}$ scooped out by moving balls of fixed radius with centers following the trajectories of the particles of a branching Brownian motion (BBM). We consider a $d$-dimensional dyadic BBM, and study the large-time asymptotic behavior of the volume of the associated branching Brownian sausage (BBM-sausage) with radius exponentially shrinking in time. Using a previous result on the density of the support of BBM, and some well-known results on the classical Wiener sausage and Brownian hitting probabilities, we obtain almost sure limit theorems as time tends to infinity on the volume of the shrinking BBM-sausage in all dimensions.
DOI: 10.1214/20-ecp316
Author: Mehmet Öz
Institution: Özyeğin University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $675
OpenAlex ID: W2990418052