包邮随机微分方程——动态系统方法(英文)

1 INTRODUCTION AND PRELIMINARIES
1．1 Stochastic Processes and Their Distributions
1．2 Semigroups of Linear Operators
1．3 Kernels and Semigroups of Kernels
1．4 Conditional Expectation， Martingales， and Markov Processes
1．5 Brownian Motion

2 ITO INTEGRALS AND STOCHASTIC DIFFERENTIAL EQUATIONS
2．1 The Ito Integral
2．2 Stochastic Differential Equations and their Solutions
2．3 Ito's Formula and Examples

3 DYNAMICAL SYSTEMS AND STOCHASTIC STABILITY
3．1 "Stochastic Dynamical Systems"
3．2 Koopman and Frobenius-Perron Operators： The Deterministic Case
3．3 Koopman and Frobenius-Perron Operators： The Stochastic Case
3．4 Liapunov Stability
3．5 Markov Semigroup Stability
3．6 Long-time behavior of a stochastic predator-prey model

BIBLIOGRAPHY

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