David — Williams Probability With Martingales Solutions Best ((free))

Its brevity means some proofs require the reader to "fill in small jumps" in arguments, which can be demanding depending on your mathematical maturity. The focus is primarily on discrete-time martingales

Elena eventually became a researcher. Years later, she recalled Williams’ own words from the preface: “I have tried to show that martingales are not just a subject, but a way of thinking.” david williams probability with martingales solutions best