The Doob decomposition theorem, proved by and named for Joseph L. Doob, is a result in the discrete-time theory of stochastic processes. It states that every adapted, integrable stochastic process can be uniquely written as the sum of a martingale and a predictable process that starts at zero.
Facts
Statementthe 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. 1 Classification
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Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Proved By
Source Doob decomposition theorem - Wikipedia
Sources
1. Doob decomposition theorem - Wikipedia
Lead section
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.
Citations section
Doob (1953), see (Doob 1990, pp. 296-298)
Lead section, statement-form reference
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.
Proved By: Joseph L. Doob, 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
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