One of the highest quality resources available online is a series of solution write-ups hosted on the blog The author has worked through a significant portion of the exercises in Williams' text.
For the most difficult exercises—especially those in the latter half of the book dealing with uniform integrability or Brownian motion—individual forum posts are invaluable. david williams probability with martingales solutions best
To guide your study, focus your solution-hunting on these foundational sections of the book: One of the highest quality resources available online
Because there is no official solution manual from David Williams or Cambridge University Press, the mathematical community has stepped in. Several highly regarded, unofficial solution sets are available online. 1. The GitHub Community Repositories It provides detailed proofs for classic problems like
Using stopping times to determine when a martingale stops being "fair."
). It provides detailed proofs for classic problems like the "Star Trek 3" and branching processes.
UI is the bridge that allows you to move limits inside expectations. Williams’ problems on UI are famously tricky, requiring precise bounding techniques. Chapter 14: Martingale Convergence Theorems