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 編輯手記