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In mathematics, Doob's martingale inequality, also known as Kolmogorov’s submartingale inequality is a result in the study of stochastic processes. It gives a bound on the probability that a submartingale exceeds any given value over a given interval of time. As the name suggests, the result is usually given in the case that the process is a ...
The optional stopping theorem can be used to prove the impossibility of successful betting strategies for a gambler with a finite lifetime (which gives condition ( a )) or a house limit on bets (condition ( b )). Suppose that the gambler can wager up to c dollars on a fair coin flip at times 1, 2, 3, etc., winning his wager if the coin comes up ...
In the theory of stochastic processes in discrete time, a part of the mathematical theory of probability, the Doob decomposition theorem gives a unique decomposition of every adapted and integrable stochastic process as the sum of a martingale and a predictable process (or "drift") starting at zero. The theorem was proved by and is named for ...
Joseph Leo Doob (February 27, 1910 – June 7, 2004) was an American mathematician, specializing in analysis and probability theory. The theory of martingales was developed by Doob. Early life and education [ edit ]
Leonard W. Doob. Leonard William Doob (March 3, 1909 – March 29, 2000) was an American academic who worked as the Sterling Professor Emeritus of Psychology at Yale University and was a pioneering figure in the fields of cognitive and social psychology, propaganda and communication studies, as well as conflict resolution.
Doob martingale. In the mathematical theory of probability, a Doob martingale (named after Joseph L. Doob, [1] also known as a Levy martingale) is a stochastic process that approximates a given random variable and has the martingale property with respect to the given filtration. It may be thought of as the evolving sequence of best ...
A CNN investigation found that Airbnb consistently fails to protect its guests despite knowing hidden cameras are a persistent concern within its industry. Airbnb’s corporate strategies ...
Doob–Meyer decomposition theorem. The Doob–Meyer decomposition theorem is a theorem in stochastic calculus stating the conditions under which a submartingale may be decomposed in a unique way as the sum of a martingale and an increasing predictable process. It is named for Joseph L. Doob and Paul-André Meyer .