●Chapter 1 Introduction
●1.1 Examples of deterministic dynamical systems
●1.2 Examples of stochastic dynamical systems
●1.3 Mathematical modeling with stochastic differential equations
●1.4 Outline of this book
●1.5 Problems
●Chapter 2 Background in Analysis and Probability
●2.1 Euclidean space
●2.2 Hilbert, Banach and metric spaces
●2.3 Taylor expansions
●2.4 Improper integrals and Cauchy principal values
●2.5 Some useful inequalities
●2.5.1 Young's inequality
●2.5.2 Gronwall inequality
●2.5.3 Cauchy-Schwarz inequality
●2.5.4 Holder inequality
●2.5.5 Minkowski inequality
●2.6 Holder spaces, Sobolev spaces and related inequalities
●2.7 Probability spaces
●2.7.1 Scalar random variables......
內容簡介
隨機動力繫統是一個入門較難的新興領域。本書是這個領域的一個較為通俗易懂的引論。在本書的**部分,作者從簡單的隨機動力繫統實際例子出發,引導讀者回顧概率論和白噪聲的基本知識,深入淺出地介紹隨機微積分,然後自然地展開隨機微分方程的討論。