Preface
Chapter 1 Introduction
1.1 Introduction
1.2 Basic
notations of probability theory
1.3 Stochastic processes
1.4 Brownian
motions
1.5 Stochastic integrals
1.6 It?o’s formula
1.7 Moment
inequalities
1.8 Gronwall-type inequalities
Chapter 2 Existence,
uniqueness and exponential stability for stochastic age-dependent
population
2.1 Introduction
2.2 Assumptions and preliminaries
2.3
Existence and uniqueness of solutions
2.3.1 Uniqueness of
solutions
2.3.2 Existence of strong solutions
2.4 Stability of strong
solutions
Chapter 3 Existence and uniqueness for stochastic age-structured
population system with diffusion
3.1 Introduction
3.2 Euler
approximation and main result
3.3 Existence and uniqueness of
solutions
3.3.1 Uniqueness of solutions
3.3.2 Existence of strong
solutions
3.4 Numerical simulation example
Chapter 4 Existence and
uniqueness for stochastic age-dependent population with fractional Brownian
motion
4.1 Introduction
4.2 Preliminaries
viii Contents
4.3
Existence and uniqueness of solutions
Chapter 5 Convergence of the Euler
scheme for stochastic functional partial differential equations
5.1
Introduction
5.2 Preliminaries and the Euler approximation
5.3 The
main results
5.4 Numerical simulation example
Chapter 6 Numerical
analysis for stochastic age-dependent
population equations
6.1
Introduction
6.2 Preliminaries and the Euler approximation
6.3 The
main results
Chapter 7 Convergence of numerical solutions to
stochastic
age-structured population system with diffusion
7.1
Introduction
7.2 Preliminaries and approximation
7.3 The main
results
7.4 Numerical simulation example
Chapter 8 Exponential
stability of numerical solutions to a stochas-
tic age-structured
population system with diffusion
8.1 Introduction
8.2 Preliminaries
and Euler approximation
8.3 The main results
8.4 Numerical simulation
example
Chapter 9 Numerical analysis for stochastic age-dependent
popula-
tion equations with fractional Brownian motion
9.1
Introduction
9.2 Preliminaries and the Euler approximation
9.3 The
main results
9.4 Numerical simulation example
Chapter 10 Convergence
of the semi-implicit Euler method for stochastic age-dependent population
equations with Markovian switching
10.1 Introduction
10.2 Preliminaries
and semi-implicit approximation
10.3 Several lemmas
Contents ix
10.4
Main results
Chapter 11 Convergence of numerical solutions to
stochastic
age-dependent population equations with Poisson jump and
Markovian switching
11.1 Introduction
11.2 Preliminaries and
semi-implicit approximation
11.3 Several lemmas
11.4 Main
results
Chapter 12 Numerical analysis for stochastic delay neural networks
with Poisson jump
12.1 Introduction
12.2 Preliminaries and the Euler
approximation
12.3 The main results
12.4 Numerical simulation
example
Chapter 13 Convergence of numerical solutions to stochastic delay
neural networks with Poisson jump and Markov
switching
13.1
Introduction
13.2 Preliminaries and the Euler approximation
13.3 Lemmas
and corollaries
13.4 Convergence with the local Lipschitz
condition
Chapter 14 Exponential stability of numerical solutions to
a
stochastic delay neural networks
14.1 Introduction
14.2
Preliminaries and approximation
14.3 Lemmas
14.4 Numerical simulation
example
Bibliography
Index
鄂公网安备 42010302001612号 