Open AccessThe Properties of Generalized Collision Branching Processes
Author(s) -
Juan Wang,
Chunhao Cai
Publication year - 2020
Publication title -
mathematical problems in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.262
H-Index - 62
eISSN - 1026-7077
pISSN - 1024-123X
DOI - 10.1155/2020/1398476
Subject(s) - collision , extinction (optical mineralogy) , uniqueness , branching (polymer chemistry) , mathematics , statistical physics , matrix (chemical analysis) , pure mathematics , mathematical analysis , physics , computer science , chemistry , optics , computer security , organic chemistry , chromatography
We consider basic properties regarding uniqueness, extinction, and explosivity for the Generalized Collision Branching Processes (GCBP). Firstly, we investigate some important properties of the generating functions for GCB q -matrix in detail. Then for any given GCB q -matrix, we prove that there always exists exactly one GCBP. Next, we devote to the study of extinction behavior and hitting times. Some elegant and important results regarding extinction probabilities, the mean extinction times, and the conditional mean extinction times are presented. Moreover, the explosivity is also investigated and an explicit expression for mean explosion time is established.