Doob–Meyer decomposition
E59636
The Doob–Meyer decomposition is a fundamental result in stochastic process theory that uniquely expresses a submartingale as the sum of a martingale and a predictable, increasing process.
All labels observed (4)
| Label | Occurrences |
|---|---|
| Doob–Meyer decomposition canonical | 6 |
| Doob–Meyer decomposition theorem | 2 |
| Doob decomposition for discrete-time submartingales | 1 |
| discrete-time Doob decomposition | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T478482 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Doob–Meyer decomposition Context triple: [Itô calculus, relatedConcept, Doob–Meyer decomposition]
-
A.
Feynman–Kac formula
The Feynman–Kac formula is a fundamental result connecting solutions of certain partial differential equations with expectations over stochastic processes, forming a bridge between quantum mechanics, probability theory, and mathematical finance.
-
B.
Kolmogorov backward equation
The Kolmogorov backward equation is a fundamental partial differential equation in stochastic processes that characterizes the time evolution of expected values of functionals of Markov processes, complementary to the Fokker–Planck (forward) equation.
-
C.
Ornstein–Uhlenbeck process
The Ornstein–Uhlenbeck process is a continuous-time stochastic process that models mean-reverting random motion, widely used in physics and quantitative finance to describe systems fluctuating around a long-term equilibrium.
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D.
Itô calculus
Itô calculus is a branch of stochastic analysis that extends classical calculus to functions of stochastic processes, particularly Brownian motion, enabling rigorous treatment of stochastic differential equations.
-
E.
Girsanov theorem
Girsanov theorem is a fundamental result in stochastic calculus that describes how the dynamics of stochastic processes, particularly Brownian motion, change under an equivalent change of probability measure.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Doob–Meyer decomposition Target entity description: The Doob–Meyer decomposition is a fundamental result in stochastic process theory that uniquely expresses a submartingale as the sum of a martingale and a predictable, increasing process.
-
A.
Feynman–Kac formula
The Feynman–Kac formula is a fundamental result connecting solutions of certain partial differential equations with expectations over stochastic processes, forming a bridge between quantum mechanics, probability theory, and mathematical finance.
-
B.
Kolmogorov backward equation
The Kolmogorov backward equation is a fundamental partial differential equation in stochastic processes that characterizes the time evolution of expected values of functionals of Markov processes, complementary to the Fokker–Planck (forward) equation.
-
C.
Ornstein–Uhlenbeck process
The Ornstein–Uhlenbeck process is a continuous-time stochastic process that models mean-reverting random motion, widely used in physics and quantitative finance to describe systems fluctuating around a long-term equilibrium.
-
D.
Itô calculus
Itô calculus is a branch of stochastic analysis that extends classical calculus to functions of stochastic processes, particularly Brownian motion, enabling rigorous treatment of stochastic differential equations.
-
E.
Girsanov theorem
Girsanov theorem is a fundamental result in stochastic calculus that describes how the dynamics of stochastic processes, particularly Brownian motion, change under an equivalent change of probability measure.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
result in probability theory
ⓘ
result in stochastic process theory ⓘ theorem ⓘ |
| appliesTo | submartingales ⓘ |
| characterizes | submartingales ⓘ |
| concludesExistenceOf |
unique martingale part
ⓘ
unique predictable increasing compensator ⓘ |
| ensures |
martingale part starts at the initial value of the submartingale
ⓘ
predictable increasing part is null at time zero ⓘ |
| field |
martingale theory
ⓘ
probability theory ⓘ stochastic processes ⓘ |
| generalizes | Lebesgue decomposition of measures in a stochastic setting ⓘ |
| hasProperty |
linearity with respect to submartingale addition and scalar multiplication
ⓘ
uniqueness up to indistinguishability ⓘ |
| hasVersion |
discrete-time Doob decomposition
ⓘ
linked to:
Doob–Meyer decomposition
|
| involvesConcept |
adapted process
ⓘ
càdlàg process ⓘ filtration ⓘ increasing process ⓘ martingale ⓘ predictable process ⓘ predictable sigma-algebra ⓘ submartingale ⓘ |
| namedAfter |
Joseph L. Doob
ⓘ
Paul-André Meyer ⓘ |
| relatedTo |
Doob decomposition for discrete-time submartingales
ⓘ
linked to:
Doob–Meyer decomposition
Girsanov theorem ⓘ Snell envelope ⓘ semimartingale decomposition ⓘ |
| requiresCondition |
integrable submartingale
ⓘ
right-continuous filtration with complete probability space ⓘ submartingale of class D for the classical version ⓘ |
| statesThat | every suitable submartingale can be written as the sum of a martingale and a predictable increasing process ⓘ |
| timeSetting | continuous time ⓘ |
| typicalAssumptionOnProcess |
adapted to a right-continuous filtration
ⓘ
càdlàg submartingale ⓘ |
| usedIn |
compensated Poisson processes
ⓘ
credit risk modeling ⓘ martingale representation theorems ⓘ mathematical finance ⓘ optional stopping and optimal stopping problems ⓘ point process theory ⓘ semimartingale theory ⓘ stochastic calculus ⓘ stochastic integration ⓘ theory of compensators ⓘ |
| yieldsDecomposition | submartingale = martingale + predictable increasing process ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Doob–Meyer decomposition Description of subject: The Doob–Meyer decomposition is a fundamental result in stochastic process theory that uniquely expresses a submartingale as the sum of a martingale and a predictable, increasing process.
Referenced by (10)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Doob–Meyer decomposition
linked to: Doob–Meyer decomposition
subject linked to:
martingale representation theorem
linked to: Doob–Meyer decomposition
linked to: Doob–Meyer decomposition