Spine decomposition for branching Markov processes and its applications

Abstract

In the literature, the spine decomposition of branching Markov processes was constructed under the assumption that each individual has at least one child. In this paper, we give a detailed construction of the spine decomposition of general branching Markov processes allowing the possibility of no offspring when a particle dies. Then we give some applications of the spine decomposition.

This is the English version of a paper to appear in a special issue of Sci. Sin. Math in honor of professor Jian-An Yan. arXiv admin note: text overlap with arXiv:1009.4481