Girsanov theorem
E9114
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.
All labels observed (4)
| Label | Occurrences |
|---|---|
| Girsanov theorem canonical | 8 |
| формула Гирсанова | 3 |
| 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.
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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.
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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.
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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.
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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
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: Girsanov theorem Description of subject: 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.
Referenced by (13)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Girsanov theorem
linked to: Girsanov theorem
linked to: Girsanov theorem
linked to: Girsanov theorem
linked to: Girsanov theorem