Limit theorems for local and occupation times of random walks and   Brownian motion on a spider
  A simple random walk and a Brownian motion are considered on a spider that is a collection of half lines (we call them legs) joined in the origin. We give a strong approximation of these two objects and their local times. For fixed number of legs we establish limit theorems on local and occupation times in n steps. 
Endre Csaki, Miklos Csorgo, Antonia Foldes and Pal Revesz
math.PR