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2020 On the volume of the shrinking branching Brownian sausage
Mehmet Öz
Electron. Commun. Probab. 25: 1-12 (2020). DOI: 10.1214/20-ECP316


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.


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Mehmet Öz. "On the volume of the shrinking branching Brownian sausage." Electron. Commun. Probab. 25 1 - 12, 2020.


Received: 6 December 2019; Accepted: 3 May 2020; Published: 2020
First available in Project Euclid: 13 May 2020

zbMATH: 1434.60249
MathSciNet: MR4112768
Digital Object Identifier: 10.1214/20-ECP316

Primary: 60D05, 60F15, 60J80, 92D25


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