On the volume of the shrinking branching Brownian sausage
| Title | On the volume of the shrinking branching Brownian sausage |
|---|---|
| Author | Öz, Mehmet |
| Publication Date: | 2020 |
| Publication Place | - The Institute of Mathematical Statistics and the Bernoulli Society |
| Subject | Branching Brownian motion, Density, Sausage, Strong law of large numbers |
| Type | Periodical |
| Language | English |
| Digital | Yes |
| Manuscript | No |
| Library: | Özyeğin University |
| Library Asset ID | 1083-589X |
| Record ID | 0336d579-6c9e-46ff-b039-f7c127fc17cf |
| Library Location | Natural and Mathematical Sciences |
| Date | 2020 |
| Sample Text | 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. |
| DOI | 10.1214/20-ECP316 |
| Cilt | 25 |
