Favourite sites of transient Brownian motion
The paper deals with the \(d\)-dimensional Brownian motion and investigates the first location of its Euclidean norm maximum. The authors derive accurate lower rate for a.s.-behavior, remember upper rate is evidently \(t\). For the transient case, i.e. \(d\geq 3\), the density of occupation time is investigated, as well. Using representation by two-dimensional Brownian motion, the lower a.s. rate is derived in that case.
scientific article; zbMATH DE number 1409165
scientific article