Stochastic Processes
Stochastic processes model how randomness evolves through time: random walks, Markov chains, Poisson arrivals and Brownian motion.
Lessons · recommended order
- 1Random WalksA sequence of iid $\pm 1$ steps whose position after $n$ steps has mean $0$ and variance $n$.Intermediate7 min
- 2Gambler's RuinFirst-step analysis for the probability and expected time to hit one of two absorbing boundaries.Intermediate9 min
- 3Markov ChainsDiscrete-state processes where the future depends only on the present, governed by a transition matrix.Intermediate8 min
- 4Poisson ProcessesA continuous-time counting process with independent increments and Poisson-distributed counts.Intermediate7 min
- 5Thinning & SuperpositionSplitting a Poisson process by independent labels, or merging independent Poisson processes, stays Poisson.Intermediate6 min
- 6Brownian MotionThe continuous-time, continuous-path limit of a random walk, with independent Gaussian increments.Advanced8 min
- 7Brownian MartingalesKey martingales built from Brownian motion that underlie option-pricing and stopping-time arguments.Advanced8 min
- 8Geometric Brownian MotionThe standard model for asset prices: constant proportional drift and volatility driving log-normal prices.Advanced8 min