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• 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