| Popis: |
This note deals with supracritical branched-chain processes. We show that the growth limitation of a chain process after a random number of generations leads to a self-similar stochastic process having the features of a statistical fractal. This transformation of the branching processes is similar to the stochastic renormalization method of Shlesinger and Hughes. Explicit conditions for the finiteness of all integer moments of the total number of active particles are derived. The renormalization leads to an increase in the critical value of the mean offspring per generation. If the number of active particles generated by an elementary process obeys a Pascal distribution, then a complete analytical solution is available. The distribution of the number of active particles has a long tail. |
