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Other online courses

Applied Stochastic Analysis

Courant, 2022 Miranda Holmes-Cerfon

  1. Review of probability theory / Introduction to Stochastic processes link
  2. Markov chains I link
  3. Markov Chains II: Detailed Balance, and Markov Chain Monte Carlo (MCMC) link
  4. Continuous-time Markov Chains link
  5. Gaussian processes & Stationary processes link
  6. Brownian motion link
  7. Stochastic Integration link
  8. Stochastic Differential Equation link
  9. Numerically solving SDEs link
  10. Forward and Backward equations for SDEs link
  11. Some applications of the backward equation link
  12. Detailed balance and Eigenfunction methods link

Stochastic Calculus

Courant, 2013 Jonathan Goodman

  1. Week 2, Discrete probability, discrete Markov chains link
  2. Week 3, Continuous time, Brownian motion and OU link
  3. Week 4, Brownian Motion and the heat equation link
  4. Week 5, Ito integral with respect to Brownian motion link
  5. Week 6, Ito's Lemma and some backward equations for Brownian motion link
  6. Week 7, General diffusions, Poisson process, backward equation link
  7. Week 8, General diffusions, part 2: Ito calculus (incomplete) link
  8. Week 9, Forward equation, generator, duality (link)[https://math.nyu.edu/~goodman/teaching/StochCalc2013/notes/Week9.pdf]
  9. Week 10, Change of measure, Girsanov link