Doob martingales are stochastic processes used in the mathematical theory of probability to approximate a given random variable. They have the martingale property and can be thought of as the best approximations to the random variable based on available information. Martingales and Azuma's inequality are the main tools used when analyzing sums, random walks, or other additive functions of non-independent random variables.
Stanford University
Fall 2022
This course dives into the use of randomness in algorithms and data structures, emphasizing the theoretical foundations of probabilistic analysis. Topics range from tail bounds, Markov chains, to randomized algorithms. The concepts are applied to machine learning, networking, and systems. Prerequisites indicate intermediate-level understanding required.
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