交互作用流的超过程PDF电子书下载

Chapter 1 From particle systems to measure-valued processes 1

1.1 Measure-valued feller processes 1

1.2 Independent particle systems:dynamical law of large numbers 3

1.3 Exchangeable particle systems 5

1.4 Random probability measures moment measures and exchangeable sequences 7

1.5 Weak convergence and the martingale problem 8

1.6 Branching particle systems 9

Chapter 2 Random measures and canonical measure-valued processes 11

2.1 State spaces for measure-valued processes 11

2.2 Random measures and laplace functions 12

2.3 Poisson cluster random measures and the canonical representation of infinitely divisible random measures 15

2.4 The structure of random measures 16

2.5 Markov transition kernels and Laplace functionals 19

2.6 Weak convergence of processes 21

Chapter 3 Construction of superprocesses arising from interacting stochastic flows 24

3.1 Introduction 24

3.2 Approximation of diffusion processes generated by Gm 27

3.3 Function-valued dual processes of SAISF 31

3.4 Branching particle systems generated by interacting stochastic flows 33

3.5 SAISF with positive continuous branching density 36

3.6 SAISF with Borel branching density 44

3.7 Examples of SAISF 52

3.8 Construction of SAISF with immigration 55

3.9 1-dimensional SAISF with measure-valued catalysts 61

Chapter 4 Probabilistic properties of superprocesses arising from stochastic flows 64

4.1 SAISF's without active underlying motions 64

4.2 Absolutely continuity and stochastic partial differential equations for the 1-dimensional SAISF with active underlying motions 72

4.3 Rescaled limits of the SAISF 78

Chapter 5 Superprocesses with branching mechanism depending on population size 82

5.1 Construction of limit dual process for SAISF depending on population size 82

5.2 Existence of SAISF depending on population size 90

5.3 Superprocesses depending on population size and the nonlinear functional of a class of 1-dimensional diffusion process 94

5.4 Some probabilistic properties of superprocesses depending on population size 101

Chapter 6 Stochastic flows of mappings 102

6.1 Notations and symbols 102

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

6.3 Construction of stochastic flows of mappings and its kernels 107

Chapter 7 State decomposition of superprocess of stochastic flows 112

7.1 Introduction 112

7.2 Martingale description 113

7.3 State decomposition of superprocess of stochastic flows 117

Bibliography 120