# Boundedness of One - Dimensional Branching Markov Processes

• F . I . KARPELEVICH, YU . M . SUHOV

#### Abstract

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

### Cite this paper

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