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交互作用流的超过程2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

交互作用流的超过程
  • 赵巧玲著 著
  • 出版社： 北京：中国农业科学技术出版社
  • ISBN：7802337695
  • 出版时间：2008
  • 标注页数：122页
  • 文件大小：52MB
  • 文件页数：130页
  • 主题词：

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图书目录

Chapter 1 From particle systems to measure-valued processes1

1.1 Measure-valued feller processes1

1.2 Independent particle systems:dynamical law of large numbers3

1.3 Exchangeable particle systems5

1.4 Random probability measures moment measures and exchangeable sequences7

1.5 Weak convergence and the martingale problem8

1.6 Branching particle systems9

Chapter 2 Random measures and canonical measure-valued processes11

2.1 State spaces for measure-valued processes11

2.2 Random measures and laplace functions12

2.3 Poisson cluster random measures and the canonical representation of infinitely divisible random measures15

2.4 The structure of random measures16

2.5 Markov transition kernels and Laplace functionals19

2.6 Weak convergence of processes21

Chapter 3 Construction of superprocesses arising from interacting stochastic flows24

3.1 Introduction24

3.2 Approximation of diffusion processes generated by Gm27

3.3 Function-valued dual processes of SAISF31

3.4 Branching particle systems generated by interacting stochastic flows33

3.5 SAISF with positive continuous branching density36

3.6 SAISF with Borel branching density44

3.7 Examples of SAISF52

3.8 Construction of SAISF with immigration55

3.9 1-dimensional SAISF with measure-valued catalysts61

Chapter 4 Probabilistic properties of superprocesses arising from stochastic flows64

4.1 SAISF's without active underlying motions64

4.2 Absolutely continuity and stochastic partial differential equations for the 1-dimensional SAISF with active underlying motions72

4.3 Rescaled limits of the SAISF78

Chapter 5 Superprocesses with branching mechanism depending on population size82

5.1 Construction of limit dual process for SAISF depending on population size82

5.2 Existence of SAISF depending on population size90

5.3 Superprocesses depending on population size and the nonlinear functional of a class of 1-dimensional diffusion process94

5.4 Some probabilistic properties of superprocesses depending on population size101

Chapter 6 Stochastic flows of mappings102

6.1 Notations and symbols102

6.2 Construction of a family of probability measures on(E,ε)103

6.3 Construction of stochastic flows of mappings and its kernels107

Chapter 7 State decomposition of superprocess of stochastic flows112

7.1 Introduction112

7.2 Martingale description113

7.3 State decomposition of superprocess of stochastic flows117

Bibliography120

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