Martingale Theory
Doob decomposition, optional stopping, and convergence theorems.
Martingale Theory. Doob decomposition, optional stopping, and convergence theorems.
Foundations and canonical references
The standard treatments of martingale theory approach the subject from complementary angles. Williams, Probability with Martingales (1991) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to.
Open methodological questions for martingale theory include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 1991Probability with Martingaleswilliams-1991
In context
Where this topic sits in the prerequisite graph. Click any node to jump.
Review this topic
This page was drafted by an agent and is waiting on expert review. Spotted a wrong prerequisite, a missing concept, a misattributed source, or a factual slip? Tell us — your review opens a tracked issue maintainers act on.