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- In short order Doob wrote Probability and Statistics in 1934, in which he sharpened then-current work of Kolmogorov and gave rigorous proofs of theorems of Fisher and Hotelling in statistics. From there he started a life-long journey in stochastic processes.
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Doob defined a stochastic process, Ω, to be measurable provided that (t, ω) → X(t, ω) is measurable on T × Ω relative to the product measure λ × P where λ is a Lebesgue measure on T . By this he meant measurable with respect to the λ × P completion of B × F or, equivalently, the λ × P completion of L × F.
- Ronald Getoor
- 2009
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After writing a series of papers on the foundations of probability and stochastic processes including martingales, Markov processes, and stationary processes, Doob realized that there was a real need for a book showing what is known about the various types of stochastic processes, so he wrote the book Stochastic Processes.
Jun 7, 2004 · Doob's work has become one of the most powerful tools available to study stochastic processes. In 1953 he published a book which gives a comprehensive treatment of stochastic processes, including much of his own development of martingale theory.
Abstract. Probability theory, and its dynamic aspect stochastic process theory, is both a venerable subject, in that its roots go back to the mid-seventeenth century, and a young one, in that its modern formulation happened comparatively recently – well within living memory.
In this sweeping review, which first appeared in French in 2000, Meyer emphasizes the founding role of Doob’s Stochastic Processes, published in 1953, which presented tools and topics that fueled probabilistic research for the rest of the century: filtrations, stopping times, martingales, Markov processes, diffusions, Itô’s stochastic ...
Sep 23, 2009 · This article is an attempt to discuss his contributions to two areas in which his work was seminal, namely, the foundations of continuous parameter stochastic processes and probabilistic potential theory.
Doob's essential contributions to Probability theory are discussed; this includes the main early results on martingale theory, Doob's h-transform, as well as a summary of Doob's three books. Finally, Doob's 'stochastic trian-gle' is viewed in the light of the stochastic analysis of the eighties. 1. Biography of J. L. Doob: Some key points.
