13. Brownian Motion and Stochastic Integral
Note
本章在原书中是一个指引性章节：连续时间金融所需的布朗运动 (Brownian motion) 与随机积分 (stochastic integral) 的数学工具，统一放在附录中展开。这里只作导引，详细内容见后续附录笔记。
Note
In the source this is a pointer chapter: the mathematical tools of continuous-time finance — Brownian motion and the stochastic integral — are developed together in the appendix. This note only serves as a signpost; see the appendix notes for the details.
参见附录：
- 第 35 章 Brownian Motion —— 布朗运动的定义与性质。
- 第 36 章 Stochastic Integral —— 关于布朗运动的伊藤积分。
- 第 37 章 Itô's Lemma —— 一元与多元伊藤引理。
以及 He (2019d) 的笔记。这些工具是第 14 章期权定价 (Option Pricing) 与第 6.3 节 ICAPM、第 9.5 节（连续时间长期风险）等内容的基础。
See the appendix:
- Chapter 35 Brownian Motion — definition and properties of Brownian motion.
- Chapter 36 Stochastic Integral — the Itô integral with respect to Brownian motion.
- Chapter 37 Itô's Lemma — the univariate and multivariate Itô's lemma.
together with the notes of He (2019d). These tools underlie Chapter 14 Option Pricing, as well as §6.3 ICAPM and §9.5 (continuous-time long-run risk).