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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Observed surface forms (1)

Surface form	Occurrences
Girsanov’s theorem	1

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 ⓘ

Referenced by (5)

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

Itô calculus → relatedConcept → Girsanov theorem ⓘ

this entity surface form: Girsanov’s theorem

Cameron–Martin theorem → relatedTo → Girsanov theorem ⓘ

Doob–Meyer decomposition → relatedTo → Girsanov theorem ⓘ

Feynman–Kac formula → relatedTo → Girsanov theorem ⓘ

Radon–Nikodym derivative → usedFor → Girsanov theorem ⓘ