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随机年龄结构种群系统(英文版)
  • 书号:9787030389206
    作者:陈兰荪
  • 外文书名:
  • 装帧:平装
    开本:B5
  • 页数:229
    字数:
    语种:en
  • 出版社:科学出版社
    出版时间:1900-01-01
  • 所属分类:O 数理科学和化学 O69 应用化学
  • 定价: ¥106.00元
    售价: ¥83.74元
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目录

  • Contents
    《生物数学丛书》序
    Preface
    Chapter 1 Introduction 1
    1.1 Introduction 1
    1.2 Basic notations of probability theory 2
    1.3 Stochastic processes 9
    1.4 Brownian motions 15
    1.5 Stochastic integrals 18
    1.6 It?o’s formula 31
    1.7 Moment inequalities 40
    1.8 Gronwall-type inequalities 45
    Chapter 2 Existence, uniqueness and exponential stability for stochastic age-dependent population 48
    2.1 Introduction 48
    2.2 Assumptions and preliminaries 49
    2.3 Existence and uniqueness of solutions 52
    2.3.1 Uniqueness of solutions 52
    2.3.2 Existence of strong solutions 53
    2.4 Stability of strong solutions 59
    Chapter 3 Existence and uniqueness for stochastic age-structured population system with diffusion 64
    3.1 Introduction 64
    3.2 Euler approximation and main result 66
    3.3 Existence and uniqueness of solutions 68
    3.3.1 Uniqueness of solutions 68
    3.3.2 Existence of strong solutions 70
    3.4 Numerical simulation example 76
    Chapter 4 Existence and uniqueness for stochastic age-dependent population with fractional Brownian motion 79
    4.1 Introduction 79
    4.2 Preliminaries 81
    4.3 Existence and uniqueness of solutions 84
    Chapter 5 Convergence of the Euler scheme for stochastic functional partial differential equations 90
    5.1 Introduction 90
    5.2 Preliminaries and the Euler approximation 91
    5.3 The main results 93
    5.4 Numerical simulation example 99
    Chapter 6 Numerical analysis for stochastic age-dependent population equations 101
    6.1 Introduction 101
    6.2 Preliminaries and the Euler approximation 102
    6.3 The main results 105
    Chapter 7 Convergence of numerical solutions to stochastic age-structured population system with diffusion 116
    7.1 Introduction 116
    7.2 Preliminaries and approximation 118
    7.3 The main results 121
    7.4 Numerical simulation example 126
    Chapter 8 Exponential stability of numerical solutions to a stochastic age-structured population system with diffusion 128
    8.1 Introduction 128
    8.2 Preliminaries and Euler approximation 130
    8.3 The main results 132
    8.4 Numerical simulation example 137
    Chapter 9 Numerical analysis for stochastic age-dependent population equations with fractional Brownian motion 140
    9.1 Introduction 140
    9.2 Preliminaries and the Euler approximation 141
    9.3 The main results 144
    9.4 Numerical simulation example 154
    Chapter 10 Convergence of the semi-implicit Euler method for stochastic age-dependent population equations with Markovian switching 156
    10.1 Introduction 156
    10.2 Preliminaries and semi-implicit approximation 157
    10.3 Several lemmas 159
    10.4 Main results 165
    Chapter 11 Convergence of numerical solutions to stochastic age-dependent population equations with Poisson jump and Markovian switching 170
    11.1 Introduction 170
    11.2 Preliminaries and semi-implicit approximation 171
    11.3 Several lemmas 173
    11.4 Main results 179
    Chapter 12 Numerical analysis for stochastic delay neural networks with Poisson jump 184
    12.1 Introduction 184
    12.2 Preliminaries and the Euler approximation 185
    12.3 The main results 187
    12.4 Numerical simulation example 195
    Chapter 13 Convergence of numerical solutions to stochastic delay neural networks with Poisson jump and Markov switching 197
    13.1 Introduction 197
    13.2 Preliminaries and the Euler approximation 198
    13.3 Lemmas and corollaries 201
    13.4 Convergence with the local Lipschitz condition 205
    Chapter 14 Exponential stability of numerical solutions to a stochastic delay neural networks 211
    14.1 Introduction 211
    14.2 Preliminaries and approximation 212
    14.3 Lemmas 214
    14.4 Numerical simulation example 220
    Bibliography 222
    Index 228
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