Doob–Meyer decomposition

E59636

result in probability theory result in stochastic process theory theorem

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.

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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

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	Doob–Meyer decomposition self-linksurface differs ⓘ surface form: discrete-time Doob 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–Meyer decomposition self-linksurface differs ⓘ surface form: Doob decomposition for discrete-time submartingales 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 ⓘ

Referenced by (10)

Full triples — surface form annotated when it differs from this entity's canonical label.

Itô calculus → relatedConcept → Doob–Meyer decomposition ⓘ

Girsanov theorem → relatedTo → Doob–Meyer decomposition ⓘ

Doob–Meyer decomposition → relatedTo → Doob–Meyer decomposition self-linksurface differs ⓘ

this entity surface form: Doob decomposition for discrete-time submartingales

Doob–Meyer decomposition → hasVersion → Doob–Meyer decomposition self-linksurface differs ⓘ

this entity surface form: discrete-time Doob decomposition

martingale representation theorem → relatedTo → Doob–Meyer decomposition ⓘ

subject surface form: Martingale representation theorem

this entity surface form: Doob–Meyer decomposition theorem

Joseph L. Doob → notableWork → Doob–Meyer decomposition ⓘ

this entity surface form: Doob–Meyer decomposition theorem

Snell envelope → associatedWith → Doob–Meyer decomposition ⓘ

Brownian filtration → usedIn → Doob–Meyer decomposition ⓘ

Paul-André Meyer → knownFor → Doob–Meyer decomposition ⓘ

Itô integral → relatedTo → Doob–Meyer decomposition ⓘ