《互動作用流的超過程》主要內容：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).
基本介紹
- 書名：互動作用流的超過程
- 出版社：中國農業科學技術出版社
- 頁數：122頁
- 開本：16
- 定價：28.00
- 作者：趙巧玲
- 出版日期：2008年12月1日
- 語種：英語
- ISBN：7802337690, 9787802337695
- 品牌：中國農業科學技術出版社
內容簡介,圖書目錄,文摘,序言,
內容簡介
《互動作用流的超過程》由中國農業科學技術出版社出版。
圖書目錄
Preface
Chapter 1 From particle systems to measure-valued processes
1.1 Measure-valued feller processes
1.2 Independent particle systems:dynamical law of large numbers
1.3 Exchangeable particle systems
1.4 Random probability measures moment measures and exchangeable sequences
1.5 Weak convergence and the martingale problem
1.6 Branching particle systems
Chapter 2 Random measures and canonical measure-valued processes
2.1 State spaces for measure-valued processes
2.2 Random measures and laplace functions
2.3 Poisson cluster random measures and the canonical representation of infinitely divisible random measures
2.4 The structure of random measures
2.5 Markov transition kernels and Laplace functionals
2.6 Weak convergence of processes
Chapter 3 Construction of superprocesses arising from interacting stochastic flows
3.1Introduction
3.2 Approximation of diffusion processes generated by Gm
3.3 Function-valued dual processes of SAISF
3.4 Branching particle systems generated by interacting stochastic flows
3.5 SAISF with positive continuous branching density
3.6 SAISF with Borel branching density
3.7 Examples of SAISF
3.8 Construction of SAISF with immigration
3.9 1-dimensional SAISF with measure-valued catalysts
Chapter 4 Probabilistic properties of superprocesses arising from stochastic flows
4.1 SAISF's without active underlying motions
4.2 Absolutely continuity and stochastic partial differential equations for the 1-dimensional SAISF with active underlying motions
4.3 Rescaled limits of the SAISF
Chapter 5 Superprocesses with branching mechanism depending on population size
5.1 Construction of limit dual process for SAISF depending on population size
5.2 Existence of SAISF depending on population size
5.3 Superprocesses depending on population size and the nonlinear functional of a class of 1-dimensional diffusion process
5.4 Some probabilistic properties of superprocesses depending on population size
Chapter 6 Stochastic flows of mappings
6.1 Notations and symbols
6.2 Construction of a family of probability measures on(E, e)
6.3 Construction of stochastic flows of mappings and its kernels
Chapter 7 State decomposition of superprocess of stochastic flows
7.1 Introduction
7.2 Martingale description
7.3 State decomposition of superprocess of stochastic flows
Bibliography
Chapter 1 From particle systems to measure-valued processes
1.1 Measure-valued feller processes
1.2 Independent particle systems:dynamical law of large numbers
1.3 Exchangeable particle systems
1.4 Random probability measures moment measures and exchangeable sequences
1.5 Weak convergence and the martingale problem
1.6 Branching particle systems
Chapter 2 Random measures and canonical measure-valued processes
2.1 State spaces for measure-valued processes
2.2 Random measures and laplace functions
2.3 Poisson cluster random measures and the canonical representation of infinitely divisible random measures
2.4 The structure of random measures
2.5 Markov transition kernels and Laplace functionals
2.6 Weak convergence of processes
Chapter 3 Construction of superprocesses arising from interacting stochastic flows
3.1Introduction
3.2 Approximation of diffusion processes generated by Gm
3.3 Function-valued dual processes of SAISF
3.4 Branching particle systems generated by interacting stochastic flows
3.5 SAISF with positive continuous branching density
3.6 SAISF with Borel branching density
3.7 Examples of SAISF
3.8 Construction of SAISF with immigration
3.9 1-dimensional SAISF with measure-valued catalysts
Chapter 4 Probabilistic properties of superprocesses arising from stochastic flows
4.1 SAISF's without active underlying motions
4.2 Absolutely continuity and stochastic partial differential equations for the 1-dimensional SAISF with active underlying motions
4.3 Rescaled limits of the SAISF
Chapter 5 Superprocesses with branching mechanism depending on population size
5.1 Construction of limit dual process for SAISF depending on population size
5.2 Existence of SAISF depending on population size
5.3 Superprocesses depending on population size and the nonlinear functional of a class of 1-dimensional diffusion process
5.4 Some probabilistic properties of superprocesses depending on population size
Chapter 6 Stochastic flows of mappings
6.1 Notations and symbols
6.2 Construction of a family of probability measures on(E, e)
6.3 Construction of stochastic flows of mappings and its kernels
Chapter 7 State decomposition of superprocess of stochastic flows
7.1 Introduction
7.2 Martingale description
7.3 State decomposition of superprocess of stochastic flows
Bibliography
文摘
插圖：
序言
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.
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.
