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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 L. Doob. The analogous theorem in the continuous-time case is the Doob–Meyer decomposition theorem.

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rdfs:label	Doob decomposition theorem (en)
rdfs:comment	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 L. Doob. The analogous theorem in the continuous-time case is the Doob–Meyer decomposition theorem. (en)
sameAs	Doob decomposition theorem Doob decomposition theorem
dbp:wikiPageUsesTemplate	dbt:' dbt:= dbt:Citation dbt:Math dbt:NumBlk dbt:Reflist dbt:EquationNote dbt:Stochastic_processes dbt:EquationRef dbt:Mathcal
Subject	Articles containing proofs Theorems regarding stochastic processes Martingale theory
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Doob_decomposition_theorem?oldid=1045047433&ns=0
Wikipage page ID	23360896 (xsd:integer)
page length (characters) of wiki page	12119 (xsd:nonNegativeInteger)
Wikipage revision ID	1045047433 (xsd:integer)
Link from a Wikipage to another Wikipage	Probability space Probability theory Risk-neutral measure Snell envelope Uniform integrability Adapted process Almost surely Monotonic function Σ-finite measure Articles containing proofs Joseph L. Doob Discounted cash flow Doob–Meyer decomposition theorem Predictable process Conditional expectation Option style Optional stopping theorem Theorems regarding stochastic processes Empty sum Equivalence (measure theory) Filtration (probability theory) Vector space Martingale theory Euclidean space Event (probability theory) Stochastic process Stopping time Lebesgue integration Martingale (probability theory) Mathematical finance Measurable function Random walk
has abstract	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 L. Doob. The analogous theorem in the continuous-time case is the Doob–Meyer decomposition theorem. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Doob_decomposition_theorem
is Link from a Wikipage to another Wikipage of	List of statistics articles List of theorems Azuma's inequality Joseph L. Doob Doob–Meyer decomposition theorem Decomposition (disambiguation)
is known for of	Joseph L. Doob
is foaf:primaryTopic of	http://en.wikipedia.org/wiki/Doob_decomposition_theorem

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