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.
Branching on a Sierpinski graph / S. Leorato, E. Orsingher. - In: STATISTICS & PROBABILITY LETTERS. - ISSN 0167-7152. - 79:2(2009), pp. 145-154.
Branching on a Sierpinski graph
S. Leorato
;
2009
Abstract
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.File | Dimensione | Formato | |
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