Joseph Leo Doob was an American mathematician, born on 27 February 1910 and died on 7 June 2004, and one of the principal architects of modern measure-theoretic probability. Building on Kolmogorov's axiomatization of probability, he established a rigorous framework for continuous-parameter stochastic processes, developed martingale theory into a central method of probability, and pioneered probabilistic potential theory. His 1953 monograph Stochastic Processes became a foundational work in the development of modern probability theory.
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Source Joseph L. Doob (Wikipedia)
Source Joseph L. Doob (Wikipedia)
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Source David Blackwell (Wikipedia)
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Source Doob decomposition theorem - Wikipedia
Source Optional Stopping Theorem (Wikipedia)
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1. Joseph L. Doob (Wikipedia)
Lead paragraph
he established a rigorous framework for continuous-parameter st
Lead paragraph [nationality-culture]
was an American mathematician
In Branch: Probability and Statistics, Lead paragraph [in-branch]
measure-theoretic probability
In Branch: Potential Theory, Lead paragraph [in-branch 2]
probabilistic potential theory
View the SourceOptional Stopping Theorem (Wikipedia)
Wikimedia FoundationProofs Credited: Optional Stopping Theorem, Lead paragraphQuote, Proofs Credited: Optional Stopping Theorem, Lead paragraph
In probability theory, the optional stopping theorem (or sometimes Doob's optional sampling theorem, for American probabilist Joseph Doob) says that, under certain conditions, the expected value
Doob decomposition theorem - Wikipedia
Proofs Credited: Doob Decomposition Theorem, Lead paragraphQuote, Proofs Credited: Doob Decomposition Theorem, Lead paragraph
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
David Blackwell (Wikipedia)
Mentored: David Blackwell, Infobox, doctoral advisor or academic advisorsView the Source Reader Challenges (0)
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