Topic: Martingale Applications

Wald’s First Identity from Indicator Sums

Wald’s Second Identity for Centered Increments

The Normalized Galton-Watson Population Martingale

Stopping Times and Integrability in Wald Problems

Sequential Sampling and Renewal Applications of Wald’s Identities

Second Moments of the Branching Population Martingale

Predictive Distributions in the Pólya Urn

Pólya Urn Proportions as Martingales

Maximal Azuma Bounds for Martingale Paths

Finite-Sample Variability in Pólya Urns