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.
One winter, Mira faced her qualifying exam. The final question: Prove that every L2 martingale admits a predictable representation with respect to an orthogonal martingale basis—essentially, decompose increments along uncorrelated directions. She remembered Williams’s voice: “Find the right projection.” Her proof unfolded: project the martingale increments onto the span of basis elements, use orthogonality to get coefficients, and show convergence in L2. Her committee applauded not just the proof but the clarity. david williams probability with martingales solutions best
Mastering David Williams’ Probability with Martingales is a rite of passage for many aspiring probabilists and quantitative analysts. While the text is celebrated for its elegance and wit, it is also notoriously challenging, often leaving readers searching for the most reliable solutions to its rigorous exercises. Why David Williams’ Text is a Classic One of the highest quality resources available online
The absence of a formal appendix with full solutions can make it difficult for independent self-study. Conciseness: While the text is celebrated for its elegance
by René Schilling: This book has full solutions to all exercises available online and is slightly more introductory than Williams Mathematics Stack Exchange from the book? Probability with Martingales - Ryan McCorvie's solutions
Some of the key concepts covered in the book include: