Gábor Tardos is a Hungarian mathematician known for his work in various areas of combinatorics, including extremal combinatorics, graph theory, and discrete mathematics. He has made significant contributions to the fields of combinatorial optimization and probability theory as well. Tardos is also recognized for his collaborative work and has published numerous research papers and articles throughout his career.
Doob's Martingale Inequality is a fundamental result in the theory of martingales, which are stochastic processes that model fair game scenarios. Specifically, Doob's inequality provides bounds on the probabilities related to the maximum of a martingale. There are a couple of versions of Doob's Martingale Inequality, but the most common one deals with a bounded integrable martingale.
Etemadi's inequality is a result in probability theory that provides a bound on the tail probabilities of a non-negative, integrable random variable. Specifically, it is used to give a probabilistic estimate concerning the sum of independent random variables, especially in the context of martingales and stopping times. The inequality states that if \( X \) is a non-negative random variable that is integrable (i.e.