The Asymptotic Behavior for Generalized Jiřina Process

As the classic branching process, Galton-Watson process has obtained intensive attentions in past decades. However, this model two idealized assumptions–discrete states and time-homogeneity. In present paper, we consider a with continuous states, for any given n∈N, law of every particle generation n is determined by population size n. We case that extinct Probability 1 since will be substantially different from size-dependent discrete states. give extinction rate sense L2 almost surely form harmonic moments, to say, show how fast {Zn−1} grows under group sufficient conditions. From result observe an asymptotic behavior mean law. The results paper have more superiority than counterpart existing literature.