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M07 · Probability II: Stochastic Processes

A free, illustrated L2 to L3 course of 10 modules in the Mathematics track. Modules include: Transformations of random variables; Moment generating and characteristic functions; The multivariate Gaussian.

M07 L2 to L3 · Intermediate to Advanced 10 modules · about 40 lessons Planned · Ring 3

Part of the Mathematics track. Ships in Ring 3 (Breadth) of the roadmap.

Modules

1. Transformations of random variables
2. Moment generating and characteristic functions
3. The multivariate Gaussian
4. Conditional expectation and the tower rule
5. Modes of convergence and limit theorems
6. Concentration inequalities
7. Markov chains
8. Poisson processes and queues
9. Random walks, martingales and Brownian motion
10. Monte Carlo methods and importance sampling

Signature illustrations

The pictures a learner should still see in their head a year later:

Gaussian ellipses under linear maps, Markov chain state diagrams settling to a stationary distribution, fans of random walks, tail-bound comparison plots.

Status

This course is planned, not written yet. It ships with Ring 3 (Breadth).

Every lesson will follow the same twelve-part blueprint with at least three purpose-made figures. Watch the repository to hear when modules ship, or help write and review it.