前辅文
Chapter 1. Introduction
§1.1. Deterministic and random differential equations
§1.2. Stochastic differentials
§1.3. Itô’s chain rule
Chapter 2. A Crash Course in Probability Theory
§2.1. Basic definitions
§2.2. Expected value, variance
§2.3. Independence
§2.4. Some probabilistic methods
§2.5. Law of Large Numbers, Central Limit Theorem
§2.6. Conditional expectation
§2.7. Martingales
Chapter 3. Brownian Motion and “White Noise”
§3.1. Motivation
§3.2. Definition, elementary properties
§3.3. Construction of Brownian motion
§3.4. Sample path properties
§3.5. Markov property
Chapter 4. Stochastic Integrals
§4.1. Preliminaries
§4.2. Itô’s integral
§4.3. Itô’s chain and product rules
§4.4. Itô’s integral in higher dimensions
Chapter 5. Stochastic Differential Equations
§5.1. Definitions, examples
§5.2. Existence and uniqueness of solutions
§5.3. Properties of solutions
§5.4. Linear stochastic differential equations
Chapter 6. Applications
§6.1. Stopping times
§6.2. Applications to PDE, Feynman–Kac formula
§6.3. Optimal stopping
§6.4. Options pricing
§6.5. The Stratonovich integral
Appendix
Exercises
Notes and Suggested Reading
Bibliography
Index
