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Mathematics

Stochastic Processes

Part of Stochastic Processes, level 7. About 46 hours of study across the topics below.

Markov Structures

  1. Stochastic Processes Basicsstate spaces, sample paths, filtrations, stationarity6.5–12 h
  2. Markov Chainstransition matrices, Chapman-Kolmogorov, invariant distributions, mixing6.5–12 h
  3. Continuous-Time Markov Chainsgenerator matrices, birth-death processes, queuing theory6.5–12 h

Continuous Processes

  1. Poisson Processesproperties, thinning, superposition, applications6.5–12 h
  2. Brownian Motionconstruction, properties, non-differentiability, scaling6.5–12 h
  3. Martingalesoptional stopping, convergence theorems, applications6.5–12 h
  4. Stochastic Calculus IntroIto integral, geometric Brownian motion, Black-Scholes intro6.5–12 h