Stochastic Simulation

This is an online companion to the lecture notes of the course Stochastic Simulation taught at Imperial College London, Department of Mathematics, by O. Deniz Akyildiz.

These pages feature extra explanations and code. Here we aim at reproduce almost every example in the notes in terms of implementation and results.

The lecture notes for the 2025-2026 (Spring) term will soon be posted (and it will be different than the last year – so please do not use the existing notes for 2024-2025).

The table of contents for this page will also be updated once the new notes are posted.

Please note that this is a work in progress. If you find any errors, please let me know.

Table of Contents

• Chapter 1 - Introduction
• Chapter 2 - Exact Generation of Random Variates
  • Section 2.1
  • Example 2.1
  • Example 2.2
  • Example 2.5
  • Example 2.6
  • Example 2.8
  • Example 2.13
  • Example 2.10
  • Example 2.13
  • Example 2.15
  • Example 2.16
• Chapter 3 - Monte Carlo Integration
  • Example 3.2
  • Example 3.3
  • Example 3.4
  • Example 3.6
  • Example 3.8
• Chapter 4 - Markov Chain Monte Carlo
  • Example 4.1
  • Example 4.2
  • Example 4.3
  • Example 4.4
  • Example 4.5
  • Example 4.6
  • Example 4.7
  • Example 4.8
  • Example 4.9
  • Example 4.10
  • Example 4.12
  • Example 4.17