Degeneracy Properties of Subcritical Branching Processes
نویسندگان
چکیده
منابع مشابه
Surviving particles for subcritical branching processes in random environment
The asymptotic behavior of a subcritical Branching Process in Random Environment (BPRE) starting with several particles depends on whether the BPRE is strongly subcritical (SS), intermediate subcritical (IS) or weakly subcritical (WS). In the (SS+IS) case, the asymptotic probability of survival is proportional to the initial number of particles, and conditionally on the survival of the populati...
متن کاملOn the survival of a class of subcritical branching processes in random environment
Let Zn be the number of individuals in a subcritical BPRE evolving in the environment generated by iid probability distributions. Let X be the logarithm of the expected offspring size per individual given the environment. Assuming that the density of X has the form pX(x) = x −β−1 l0(x)e −ρx for some β > 2, a slowly varying function l0(x) and ρ ∈ (0, 1) , we find the asymptotic survival probabil...
متن کاملLimit Theorems for Subcritical Age-dependent Branching Processes with Two Types of Immigration
For the classical subcritical age-dependent branching process the effect of the following two-type immigration pattern is studied. At a sequence of renewal epochs a random number of immigrants enters the population. Each subpopulation stemming from one of these immigrants or one of the ancestors is revived by new immigrants and their offspring whenever it dies out, possibly after an additional ...
متن کاملBranching processes in random environment – a view on critical and subcritical cases
Branching processes exhibit a particularly rich longtime behaviour when evolving in a random environment. Then the transition from subcriticality to supercriticality proceeds in several steps, and there occurs a second ‘transition’ in the subcritical phase (besides the phase-transition from (sub)criticality to supercriticality). Here we present and discuss limit laws for branching processes in ...
متن کاملBranching Processes
Galton-Watson processes were introduced by Francis Galton in 1889 as a simple mathematical model for the propagation of family names. They were reinvented by Leo Szilard in the late 1930s as models for the proliferation of free neutrons in a nuclear fission reaction. Generalizations of the extinction probability formulas that we shall derive below played a role in the calculation of the critica...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Annals of Probability
سال: 1973
ISSN: 0091-1798
DOI: 10.1214/aop/1176996893