Research On The Related Properties Of Collisional Branching Process

In this paper, the related properties of collision branching process are dis-cussed and studied, and some related conclusions about the existence of duality,monotonicity, extinction probability and quasi-stationary distribution of collision branching are introduced.The first chapter is the introduction part of this article, branching process is introduced, the research background and significance of collision branching pro-cess, research history and research status quo and the main work done in this paper.The second chapter is the preliminary knowledge of this article,this paper introduces the continuous time Markov chain and the related definition and theory of collision branching process.The third chapter is the core part of this paper, introducing the collision branch model, the regularity, the existence uniqueness, the monotone and the du-ality, proving the sufficient condition of the probability 1 extinction with another method,the existence of the quasi-stationary distribution, Correlated Second Or-der Differential Equations for Stable Distribution Probability Expressions.The fourth chapter is a summary and prospect. Although we construct a sec-ond order differential equation for solving the quasi-stationary distribution prob-ability expression, we do not get the effective solution to the equation. At the end of this chapter, the quasi-stationary distribution of the collision branch process Probability form gives a conjecture, hoping to gather everyone's wisdom,the col-lision branch of the process of quasi-stable distribution of the nature of a better perfection.