Öz, Mehmet2021-02-082021-02-0820201083-589Xhttp://hdl.handle.net/10679/7277https://doi.org/10.1214/20-ECP316The 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.engopenAccessarticle2511200053589980000110.1214/20-ECP316Branching Brownian motionDensitySausageStrong law of large numbers2-s2.0-85087071155