📈 Stochastic Differential Equations (SDE)

"Probability is not about the odds, but about the flow of information."

📊 Course Metadata

• Department: School of Mathematical Sciences, Zhejiang University

• Prerequisites: Mathematical Analysis, Ordinary Differential Equations (ODE), Real Analysis, Probability Theory, Stochastic Processes, Functional Analysis (Recommended)

• Course Type: 32-hour Graduate Course

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📚 References & Literature

This course does not utilize slides; it is taught entirely via hand-written board lectures by the professor.

1. Jianli Liu & Hairong Yuan, Basic Theory and Applications of Stochastic Differential Equations

   • Instructor's Comment: This book is relatively entry-level.

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🗺️ Course Map (Syllabus & Navigation)

Below is the detailed directory for the course notes:

Part I: Probability Theory and Brownian Motion

• Chapter 1: Conditional Expectation

• Chapter 2: Brownian Motion

Part II: Stochastic Integration and SDEs

• Chapter 3: Stochastic Integration

• Chapter 4: Itô Integration

• Chapter 5: Multivariate Itô Integral and Stochastic Differential Equations

• Chapter 6: Existence and Uniqueness Theorem

Part III: Applications of SDEs

• Chapter 7: Option Pricing and Stopping Times

Part IV: 📝 Selected Solutions

• Chapter 1-2 Solutions： Conditional Expectation and Brownian Motion

• Chapter 3-4 Solutions： Stochastic Integrals and Itô's Formula

• Chapter 5-6 Solutions： ultivariate Itô's Formula and SDE Solving in Practice

• Chapter 7 Solutions: Option Pricing and Stopping Times

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📝 Notes & Formatting Details

Construction Complete

This page is now substantially complete. Long theorems and exercise solutions in the notes feature a folded box design. If you spot any typos, please feel free to raise an Issue or contact me directly for corrections!

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