Phase 4: Math → Code Bridge · ~75 minutes · Python
Stochastic Processes
Randomness with structure. The math behind random walks, Markov chains, and diffusion models.
What you will learn
- Simulate 1D and 2D random walks and verify the sqrt(n) scaling of displacement
- Build a Markov chain simulator and compute its stationary distribution via eigendecomposition
- Implement Metropolis-Hastings MCMC and Langevin dynamics for sampling from target distributions
- Connect the forward diffusion process to Brownian motion and explain how the reverse process generates data
Introduction
- Type: Learn
- Language: Python
- Prerequisites: Probability and Distributions, Bayes' Theorem
- Time: ~75 minutes
Objective
Learning objectives
- Simulate 1D and 2D random walks and verify the sqrt(n) scaling of displacement
- Build a Markov chain simulator and compute its stationary distribution via eigendecomposition
- Implement Metropolis-Hastings MCMC and Langevin dynamics for sampling from target distributions
- Connect the forward diffusion process to Brownian motion and explain how the reverse process generates data
Unlock the full lesson
You've read the first 2 sections. The rest of this lesson covers The Problem, The Concept, Build, Check Yourself, Key Terms & Next — plus a hands-on lab, quiz, and project artifact.
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