交互作用流的超过程

出版时间：2008-12  出版社：中国农业科学技术出版社  作者：赵巧玲  页数：122  

内容概要

　　This paper is divided into 7 chapters．The central theme of these lectures is the construction and study of a new class of superpro-cesses named as“superprocesses arising from interacting stochastic flows”(abbreviated to SAISF).

书籍目录

PrefaceChapter 1  From particle systems to measure-valued processes1.1  Measure-valued feller processes1.2  Independent particle systems:dynamical law of large numbers1.3  Exchangeable particle systems1.4  Random probability measures moment measures and exchangeable sequences1.5  Weak convergence and the martingale problem1.6  Branching particle systemsChapter 2  Random measures and canonical measure-valued processes2.1  State spaces for measure-valued processes2.2  Random measures and laplace functions2.3  Poisson cluster random measures and the canonical representation of infinitely divisible random measures2.4  The structure of random measures2.5  Markov transition kernels and Laplace functionals2.6  Weak convergence of processesChapter 3  Construction of superprocesses arising from interacting stochastic flows3.1　 Introduction3.2  Approximation of diffusion processes generated by Gm3.3  Function-valued dual processes of SAISF3.4  Branching particle systems generated by interacting stochastic flows3.5  SAISF with positive continuous branching density3.6  SAISF with Borel branching density3.7  Examples of SAISF3.8  Construction of SAISF with immigration3.9  1-dimensional SAISF with measure-valued catalystsChapter 4  Probabilistic properties of superprocesses arising from stochastic flows4.1  SAISF's without active underlying motions4.2  Absolutely continuity and stochastic partial differential equations for the 1-dimensional SAISF with active underlying motions4.3  Rescaled limits of the SAISFChapter 5  Superprocesses with branching mechanism depending on population size5.1  Construction of limit dual process for SAISF depending on population size5.2  Existence of SAISF depending on population size5.3  Superprocesses depending on population size and the nonlinear functional of a class of 1-dimensional diffusion process5.4  Some probabilistic properties of superprocesses depending on population sizeChapter 6  Stochastic flows of mappings6.1  Notations and symbols6.2  Construction of a family of probability measures on(E, e)6.3  Construction of stochastic flows of mappings and its kernelsChapter 7  State decomposition of superprocess of stochastic flows7.1　 Introduction7.2  Martingale description7.3  State decomposition of superprocess of stochastic flowsBibliography

章节摘录

　　This paper is divided into 7 chapters.　　The central theme of these lectures is the construction and study of a new class of superpro-cesses named as"superprocesses arising from interacting stochastic flows" （ abbreviated to SAISF）.　　In Chapter 1 -Chapter 2, we will introduction some elementary theories about measure-val-ued processes.　　In Chapter 3, we will construct a new class of superprocesses named as" superprocesses ari-sing from interacting stochastic flows"（ abbreviated to SAISF）. These superprocesses are charac-terized by their generators as:　　This class of superprocesses is the unified setting of some new born classes of superprocessesconsidered by many authors in their papers. Here we use the duality method developed by Daw-son, Li and Wang to prove their strong Markov property and the technique of branching particlesystem approximation to prove their existence. In the end of this chapter, we shall give some vari-ance of this class of superprocesses.　　in Chapter 4, we shall investigate its probabilistic properties.Firstly, we shall prove theatomic property of the SAISF if its parameters satisfies the condition that ap（ x, x） = cp'q （x） forany xin Section 4. 1. Secondly, we will deduce the stochastic partial differential equationassociated with 1 -dimensional SAISF in Section 4.2. Thirdly, we will consider some rescaled limitfor the SAISF under some conditions.　　In Chapter 5 ,we will use" piecing" technique to investigate the SAISF with branching mecha-nism depending on population size and general superprocesses with branching mechanism depen-ding on population size. The limit duality method and "piecing" technique are main methods inthis chapter.　　In Chapter 6, the stochastic flow of mappings generated by a Feller convolution semigroup ona compact metric space is studied. This kind of flow is the generalization of superprocesses of sto-chastic flows and stochastic diffeomorphism induced by the strong solutions of stochastic differenti-al equations. 　　……