Lecture 2 ( Edinburgh ) : BPRE and properites of random walk
نویسنده
چکیده
1 Branching processes in random environment In this lecture fundamental properties of branching processes in a random environment are developed. In such a process individuals reproduce independently of each other according to random offspring distributions which vary from one generation to the other. To give a formal definition let P = {π} be the space of probability measures on N 0 Equipped with the metric of total variation P becomes a Polish space. With each π we assiciate the respective probability generating function f (s) = ∞ i=0 π {i} s i (1) and let F be the set of such generating functions. Let Π be a random variable (probability distribution) taking values in P, or, what is the same, a random probability generating function F.
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Limit theorems for subcritical Branching Process in Random Environment depending on the initial number of particles
Asymptotic behaviors for subcritical Branching Processes in Random Environment (BPRE) starting with several particles depend on whether the BPRE is strongly subcritical (SS), intermediate subcritical (IS) or weakly subcritical (WS) (see [12]). Descendances of particles for BPRE are not independent. In the (SS+IS) case, the asymptotic probability of survival is proportional to the initial number...
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