Girsanov theorem

E9114

result in stochastic calculus 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.

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All labels observed (3)

Label	Occurrences
Girsanov theorem canonical	8
Girsanov transformation	1
Girsanov’s theorem	1

How this entity was disambiguated

This entity first appeared as the object of triple T100607 — 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: Girsanov theorem
Context triple: [Feynman–Kac formula, relatedTo, Girsanov theorem]

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. Fokker–Planck equation
The Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability density function of a stochastic (random) process, such as Brownian motion.
C. Feynman–Hellmann theorem
The Feynman–Hellmann theorem is a result in quantum mechanics that relates the derivative of an energy eigenvalue with respect to a parameter in the Hamiltonian to the expectation value of the corresponding derivative of the Hamiltonian.
D. Einstein–Smoluchowski relation
The Einstein–Smoluchowski relation is a fundamental equation in statistical physics that links the diffusion coefficient of particles undergoing Brownian motion to their mobility and thermal energy.
E. Brownian motion
Brownian motion is the random, jittery movement of microscopic particles suspended in a fluid, whose explanation provided key evidence for the existence of atoms and the molecular nature of matter.
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: Girsanov theorem
Target entity description: 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.

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. Fokker–Planck equation
The Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability density function of a stochastic (random) process, such as Brownian motion.
C. Feynman–Hellmann theorem
The Feynman–Hellmann theorem is a result in quantum mechanics that relates the derivative of an energy eigenvalue with respect to a parameter in the Hamiltonian to the expectation value of the corresponding derivative of the Hamiltonian.
D. Einstein–Smoluchowski relation
The Einstein–Smoluchowski relation is a fundamental equation in statistical physics that links the diffusion coefficient of particles undergoing Brownian motion to their mobility and thermal energy.
E. Brownian motion
Brownian motion is the random, jittery movement of microscopic particles suspended in a fluid, whose explanation provided key evidence for the existence of atoms and the molecular nature of matter.
F. None of above. chosen

Statements (49)

Predicate	Object
instanceOf	result in stochastic calculus ⓘ theorem ⓘ
appliesTo	Brownian motion ⓘ Itô processes ⓘ continuous-time stochastic processes ⓘ semimartingales ⓘ
category	theorems in probability theory ⓘ theorems in stochastic processes ⓘ
concerns	adapted processes ⓘ semimartingale characteristics ⓘ
coreConcept	Radon–Nikodym derivative ⓘ drift transformation ⓘ equivalent change of probability measure ⓘ exponential martingale ⓘ martingale measure ⓘ
describes	change of dynamics of stochastic processes under change of measure ⓘ how Brownian motion changes under an equivalent change of probability measure ⓘ
enables	construction of equivalent martingale measures ⓘ removal of drift from stochastic differential equations by measure change ⓘ
field	probability theory ⓘ stochastic analysis ⓘ stochastic calculus ⓘ
formalizedIn	measure-theoretic probability ⓘ
generalizes	change-of-measure techniques in classical probability ⓘ
holdsOn	filtered probability spaces ⓘ
implies	drift terms can be removed or introduced by changing measure ⓘ local martingales under one measure may become martingales under another ⓘ
namedAfter	Igor Vladimirovich Girsanov ⓘ
relatedTo	Cameron–Martin theorem ⓘ Doob–Meyer decomposition ⓘ Feynman–Kac formula ⓘ martingale representation theorem ⓘ
requires	Novikov condition or similar integrability condition ⓘ absolute continuity of measures on the underlying filtration ⓘ existence of an equivalent probability measure ⓘ
statesThat	a process that is Brownian motion under one measure becomes a Brownian motion with drift under another equivalent measure ⓘ under an equivalent change of measure the Brownian motion acquires a drift term ⓘ
typicalAssumption	Brownian motion with respect to a given filtration ⓘ integrability of the drift process ⓘ
usedIn	change from physical measure to risk-neutral measure ⓘ derivative pricing ⓘ filtering theory ⓘ large deviations theory ⓘ mathematical finance ⓘ risk-neutral valuation ⓘ stochastic control ⓘ
uses	Itô calculus ⓘ Radon–Nikodym derivative to define new measure ⓘ stochastic exponentials ⓘ

How these facts were elicited

Referenced by (10)

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

Feynman–Kac formula → relatedTo → Girsanov theorem ⓘ

Itô calculus → relatedConcept → Girsanov theorem ⓘ

this entity surface form: Girsanov’s theorem

Doob–Meyer decomposition → relatedTo → Girsanov theorem ⓘ

Radon–Nikodym derivative → usedFor → Girsanov theorem ⓘ

Cameron–Martin theorem → relatedTo → Girsanov theorem ⓘ

Igor Vladimirovich Girsanov → notableFor → Girsanov theorem ⓘ

Igor Vladimirovich Girsanov → notableConcept → Girsanov theorem ⓘ

this entity surface form: Girsanov transformation

Clark–Ocone formula → relatedTo → Girsanov theorem ⓘ

Brownian filtration → usedIn → Girsanov theorem ⓘ

Wiener measure → playsRoleIn → Girsanov theorem ⓘ

All labels observed (3)

How this entity was disambiguated Show

Statements (49)

How these facts were elicited Show

Referenced by (10)

How this entity was disambiguated

How these facts were elicited