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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.〔, see 〕 The analogous theorem in the continuous-time case is the Doob–Meyer decomposition theorem. ==Statement of the theorem== Let be a probability space, } with or a finite or an infinite index set, a filtration of , and an adapted stochastic process with for all . Then there exists a martingale and an integrable predictable process starting with such that for every . Here predictable means that is -measurable for every }. This decomposition is almost surely unique. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Doob decomposition theorem」の詳細全文を読む スポンサード リンク
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