Courant, 2022 Miranda Holmes-Cerfon
- Review of probability theory / Introduction to Stochastic processes link
- Markov chains I link
- Markov Chains II: Detailed Balance, and Markov Chain Monte Carlo (MCMC) link
- Continuous-time Markov Chains link
- Gaussian processes & Stationary processes link
- Brownian motion link
- Stochastic Integration link
- Stochastic Differential Equation link
- Numerically solving SDEs link
- Forward and Backward equations for SDEs link
- Some applications of the backward equation link
- Detailed balance and Eigenfunction methods link
Courant, 2013 Jonathan Goodman
- Week 2, Discrete probability, discrete Markov chains link
- Week 3, Continuous time, Brownian motion and OU link
- Week 4, Brownian Motion and the heat equation link
- Week 5, Ito integral with respect to Brownian motion link
- Week 6, Ito's Lemma and some backward equations for Brownian motion link
- Week 7, General diffusions, Poisson process, backward equation link
- Week 8, General diffusions, part 2: Ito calculus (incomplete) link
- Week 9, Forward equation, generator, duality (link)[https://math.nyu.edu/~goodman/teaching/StochCalc2013/notes/Week9.pdf]
- Week 10, Change of measure, Girsanov link