测度值分枝过程与移民过程

本文介绍了测度值分枝过程和由斜卷积半群定义的伴随移民过程的基本理论和研究现状,主要内容包括：分枝粒子系统的收敛;超过程的基本正则性和极限定理;非线性微分方程;广义分枝模型;斜卷积半群和进入律;用Ｋｕｚｎｅｔｓｏｖ过程构造移民过程等。     

球面介质作用下的测度值分枝过程

我们考虑空间上一粒子系统，当其受到分布于求面上的介质作进行粒子分枝和衍生，产生新了体，而新粒子仍按原粒子的运动规则继续空间运动。通过合理的假设和极限过程，粒子在空间的散布一测度值分枝过程来刻划。     

测度值分枝扩散过程在球域上负荷的概率估计

本文通过对一类非线性微分方程解的性质研究，给出了测度值分枝扩散过程在球域上负荷概率的精确估计     

交互测度值过程

具有交互作用的测度值分枝过程是当今测度值马氏过程的研究热点之一。本文系统介绍了这一领域的最新进展,针对一些关键的思想、方法及国内在测度值过程研究的情况做了简单评述,并且列举了若干未解决的问题。     

Euler方程组的凝聚和测度值解

引入了解的凝聚，Ｙｏｕｎｇ测度和测量度值解的概念，建立了由渐近解序列生成测度值解的定理。     

一类奇异情形的测度值过程

构造了一类描述在R^d中测度如何在随机流或``虚流''''下演化的测度值过程. 一方面可视此类过程为测度值流, 另一方面已有的可测映射流、核的流的框架不能覆盖此类过程.     

集值增过程产生的集值测度

本文首先研究集值增函数在B(R+)上产生的集值测度,然后在其基础上研究集值增过程A(ω,t),(ω,t)∈Ω×R+,在乘积可测空间F×B(R+)上产生的集值测度,在一定条件下建立了两者之间的一一对应关系.     

随机环境中分枝q-过程

引进了机环境中一致马氏过程,随机分枝q-矩阵和随机环境中分枝q-过程.给了随机环境中分枝q-过程存在性和唯一性的充分条件.最后证明了任意随机分枝转移密度矩阵都是零流入的.     

广义分枝过程的强遍历性

在文[1]的基础上，进一步讨论了广义分枝Q－矩阵的强遍历性及随机单调性。     

两参数广义碰撞分枝过程

本文考虑一类新的分枝过程：两参数碰撞分枝过程.对于这类过程,建立了正则性和唯一性判别准则.给出了两个吸收态的吸收概率和吸收时间的精确表达式.同时,给出了爆炸概率、爆炸时间以及全局逗留时间的精确表达式,揭示了次爆炸情形和超爆炸情形的不同性质.     

Branching Processes with Immigration and Related Topics

This is a survey on the recent progresses in the study of branching processes with immigration, generalized Ornstein-Uhlenbeck processes, and affine Markov processes. We mainly focus on the applications of skew convolution semigroups and the connections in those processes.     

Uniqueness and Extinction of Weighted Markov Branching Processes

This paper focuses on discussing some basic properties of the weighted Markov branching process which is a natural generalisation of the ordinary Markov branching process. The regularity and uniqueness criteria, which are very easy to verify, are firstly established. Some important characteristics regarding the hitting times of such structure are obtained. In particular, the closed forms for the mean extinction time and conditional mean extinction time are presented. The explosion behaviour of the process is investigated and then the mean explosion time is derived. The mean global holding time and the mean total survival time are also obtained. AMS 2000 Subject Classification Primary 60 J27; Secondary 60 J80     

Asymptotic Behaviors for Critical Branching Processes with Immigration

In this paper, we investigate the asymptotic behaviors of the critical branching process with immigration {Z_n, n ≥ 0}. First we get some estimation for the probability generating function of Zn. Based on it, we get a large deviation for Z_(n+1)/Z_n. Lower and upper deviations for Zn are also studied. As a by-product, an upper deviation for max_(1≤i≤n) Z_i is obtained.     

随机环境中依赖年龄分枝过程的爆炸问题

讨论了随机环境中依赖年龄分枝过程中的爆炸问题,得到了过程爆炸的判定定理以及关于两个过程爆炸的比较定理.     

Absolute Continuity of Measures in the Class of Markov and Semi-Markov Processes of Diffusion Type

The property of absolute continuity of measures in the class of one-dimensional semi-Markov processes of diffusion type is investigated. The measure of such a process can be composed of two measures. The first one is a distribution of a random track, and the second one is a conditional distribution of a time run along the track. The desired density is represented in the form of product of two corresponding densities.     

Limit Processes for Age-Dependent Branching Particle Systems

We consider systems of spatially distributed branching particles in R ^d . The particle lifelengths are of general form, hence the time propagation of the system is typically not Markov. A natural time-space-mass scaling is applied to a sequence of particle systems and we derive limit results for the corresponding sequence of measure-valued processes. The limit is identified as the projection on R ^d of a superprocess in R ₊×R ^d . The additive functional characterizing the superprocess is the scaling limit of certain point processes, which count generations along a line of descent for the branching particles.     

Functional limit theorems for the “disorder” problem

Let X ⁽ⁿ⁾=(X _k ), 1≦k≦n be random process with discrete time defined by its transition probabilities which belong to some parametric family. It is assumed that the parameters of the transition probabilities before and/or after disorder as well as the disorder time, are unknown. For statistical purposes the processes of Radon-Nikodym derivatives of the measures generated by processes with disorder at the time s with respect to the measure generated by process without disorder where 1≦s≦n are often used. In the paper general sufficient conditions are given for weak convergence of these processes. Some examples are given to illustrate the application of the results obtained.     

随机环境中受控两性分枝过程的概率性质

本文介绍了一类配对依赖人口数的随机环境中受控两性分枝过程,研究了它的马氏性,对偶律及其概率母函数的性质.     

带移民的碰撞分枝过程的唯一性

本文提出了一种带移民的碰撞分枝过程,它由三部分组成:马氏分枝过程、碰撞分枝过程和状态独立的移民过程,给出了该过程正则性和唯一性判别准则。