Branching on a Sierpinski graph

The descending motion of particles in a Sierpinski gasket subject to a branching process is examined. The splitting on escape nodes of falling particles makes the event of reaching the base of the gasket possible with positive probability. The r.v.'s Y (k), representing the number of particles reaching level k (that is the k-th generation) is the main object of our analysis. The transition probabilities, the means and variances of Y (k) are obtained explicitly with a number of recursive formulas concerning the probability generating functions E tY (k), k ≥ 1. A section is also devoted to the analysis of extinction probabilities for the branching process developing in this specific fractal set.