Topic: Martingale Inequalities and Convergence

Worked Problems in Martingale Inequalities and Convergence

Using Upcrossing Bounds to Diagnose Oscillation

Upcrossings of a Real-Valued Sequence

Upcrossings and Almost-Sure Convergence

Uniform Integrability Versus Bounded First Moments

Uniform Integrability Through Tail Expectations

Uniform Integrability and L1 Convergence

The Pathwise Upcrossing Inequality

The Martingale Convergence Theorem Under Uniform Integrability

The L2 Variance Decomposition