Chapter 1. Random Walk and Discrete Heat Equation
1.2. Boundary value problems
1.4. Expected time to escape
1.5. Space of harmonic functions
Chapter 2. Brownian Motion and the Heat Equation
2.6. More on harmonic functions
2.7. Constructing Brownian motion
3.2. Conditional expectation
3.3. Definition of martingale
3.4. Optional sampling theorem
3.5. Martingale convergence theorem
3.6. Uniform integrability
Chapter 4. Fractal Dimension
4.3. Hausdorff measure and dimension