带有迁移的超过程的一些性质

本文从带有迁移的分枝粒子系统出发，建立了底过程的Ｊ—泛函与超过程的可加泛函的对应关系，并且得到了占位时过程的拉氏泛函表达式．     

一般介质下的超过程的研究

本文考虑一般介质作用下的分枝粒子系统，进而建立了一类比较广泛分枝机制下的超布朗运动．同时本文研究了这类超过程的轨道性质．亦即证明了其轨道连续性和局部绝对连续性     

两物种超过程分枝特征的刻画

本文运用调和分析的方法，通过对二元连续函数的积分表示问题的研究，得到了一类两物种超过程的分枝特征的一般刻画。     

一类流动介质下超过程占位时的状态特征

本文考虑流动介质下的粒子系统，在Ｄａｗｓｏｎ假设下引出一类带广义分枝的测度值分枝过程（超过程）．这类超过程描述了更丰富的粒子分枝现象，具有许多独特的性质．在此我们主要研究其积分过程即占位时过程，揭示了它的两个重要特性即密度场的存在性和长时间的收敛性．     

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。     

随机环境中的多物种分枝游动

本文建立了随机环境中多物种分枝游动模型，研究了这一模型的有关质点密度问题。证明了大范围平均j-型质点密度和大范围平均质点密度均是以指数速度增长的，且明确地给出了增长指数。     

竞争性生态系统中两物和中的共存问题

利用Ｂａｎａｃｈ空间中锥与半序理论研究了竞争性生态系统中两物种的共存问题，得出依赖于某一共同生存环境的两物种在一定条件下必可达唯一共存状态。     

多物种无穷维反应扩散粒子系统鞅解的唯一性

本文利用鞅方法以及停时、耦合等技巧,并通过构造一族随时间而变化的有穷维上的多物种反应扩散粒子系统的鞅解来做无穷维逼近,证明了多物种无穷维反应扩散粒子系统鞅解的唯一性。     

带竞争的分枝粒子系统和相关的极限定理

本文用随机积分方程构造了一类带竞争的分枝粒子系统;研究了相关的鞅性质;并且证明了当参数满足一定条件时,重整化之后的粒子系统序列中任何的极限点均为满足一特定鞅问题的超过程.这些推广了Fournier和Mlard(2004)的部分结果.     

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。     

Forward Feynman-Kac type representation for semilinear non-conservative partial differential equations

ABSTRACT

We propose a non-linear forward Feynman-Kac type equation, which represents the solution of a nonconservative semilinear parabolic Partial Differential Equations (PDE). We show in particular existence and uniqueness. The solution of that type of equation can be approached via a weighted particle system.     

Holomorphic Bogoliubov functionals for interacting particle systems in continuum

Combinatorial harmonic analysis techniques are used to develop new analytical methods for the study of interacting particle systems in continuum based on a Bogoliubov functional approach. Concrete applications of the methods are presented, namely, conditions for the existence of Bogoliubov functionals, a uniqueness result for Gibbs measures in the high temperature regime. We also propose a new approach to the study of non-equilibrium stochastic dynamics in terms of evolution equations for Bogoliubov functionals.     

Numerical method of lines for parabolic functional differential equations

Initial boundary value problems for nonlinear parabolic functional differential equations are transformed by discretization in space variables into systems of ordinary functional differential equations. A comparison theorem for differential difference inequalities is proved. Sufficient conditions for the convergence of the numerical method of lines are given. An explicit Euler method is proposed for the numerical solution of systems thus obtained. This leads to difference scheme for the original problem. A complete convergence analysis for the method is given.     

中立型泛函微分方程的周期解

对于中立型泛函微分方程,证明了解的毕竟有界性蕴含周期解的存在性,把常微分方程中著名的Yoshizawa周期解存在定理推广到中立型泛函微分方程,然后利用所得结果给出一类产生于电力系统的中立型时滞泛函微分方程周期解存在惟一与吸引的条件。     

Translation Continuous Functionals on CB(ℝ) and Their Supports

Two constructions of translation continuous functionals on the space of bounded continuous functions on a locally compact group are introduced and the properties of these functionals related to the notion of support of a functional are considered.     

Approximative solution of the coagulation–fragmentation equation by stochastic particle systems

This paper studies stochastic particle systems related to the coagulation fragmentation equation. For a certain class of unbounded coagulation kernels and fragmentation rates, relative compactness of the stochastic systems is established and weak accumulation points are characterized as solutions. These results imply a new existence theorem. Finally a simulation algorithm based on the particle systems is proposed     

Ivlev型捕食系统的全局动力学分析

研究捕食者与食饵均具有线性密度制约的Ivlev型捕食动力系统.应用常微分方程定性方法,得到了正平衡点的全局稳定性和非小振幅极限环的存在唯一性的充分条件.特别地,在一定条件下,证明了极限环的存在唯一性与正平衡点的局部不稳定性是等价的,正平衡点的局部稳定性隐含它的全局稳定性,因此,系统的全局动力学性质完全由正平衡点的局部性质所决定.     

Functional large deviations for burgers particle systems

We consider Burgers particle systems, i.e., one‐dimensional systems of sticky particles with discrete white‐noise‐type initial data (not necessarily Gaussian), and describe functional large deviations for the state of the systems at any given time. For specific functionals such as maximal particle mass, particle speed, rarefaction interval, momentum, and energy, the research was initiated by Avellaneda and E [1, 2] and pursued further by Ryan [14]. Our results extend those of Ryan and contain many other examples. © 2006 Wiley Periodicals, Inc.     

Hybrid systems: Modelling and analysis using emergent dynamics

In this paper, we discuss modelling and analysis of hybrid systems with physical interaction dynamics. Such systems are typically considered complex and they are modelled using abstractions. Abstractions may, however, unintentionally exclude critical details, leading to partial or false results. Therefore, we study here use of a particle system in modelling and analysis. The novelty of the particle system is that it is designed to reveal interaction dynamics as emergent dynamics; thus, supporting analysis of complex and intricate interaction dynamics with acceptable modelling effort. As the main contribution, we formalize the particle system, and use it to model and analyze hybrid systems, both mechanical and biological, with nontrivial interaction dynamics.     

Couplages croissants pour les systèmes de particles interactives

Classical stochastic comparison results for spin systems are generalized to more complex interacting particle systems. The state space of each site is a finite partially ordered set and several sites may simultaneously change status. Two ways of obtaining comparison conditions are considered. The first one consists in adapting to interacting particle systems a result by Massey for Markov processes on countable spaces. The second is based on the explicit construction of Markov couplings. In particular, a generalization of the Vasershtein coupling for spin systems is used.