to be finite. Here Ek(t is the position of the kth particle, and N(t) is the size of the population at time t. For some classes of processes (smooth branching diffusions with Feller-type boundary points), this results in a () ,,, criterion stated in terms of the linear ODE 2 (x)+a(x)Z’(x),(x)(1-(x))f(x). Here or(x) and a(x) are the diffusion coefficient and the drift of the one-particle diffusion, respectively, and ,(x) and (x) the intensity of branching and the expected number of offspring at point x, respectively. Similarly, for branching jump Markov processes the conditions

@inproceedings{KARPELEVICHBoundednessOO,
title={Boundedness of One - Dimensional Branching Markov Processes},
author={F . I . KARPELEVICH and YU . M . SUHOV}
}