On the volume of the shrinking branching Brownian sausage
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Type :
Article
Publication Status :
Published
Access :
openAccess
Abstract
The branching Brownian sausage in R-d was defined in [4] similarly to the classical Wiener sausage, as the random subset of 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.
Source :
Electronic Communications in Probability
Date :
2020
Volume :
25
Publisher :
The Institute of Mathematical Statistics and the Bernoulli Society
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