Disambiguation evidence for martingale representation theorem via surface form
"Martingale representation theorem"
As subject (45)
Triples where this entity appears as subject under the
label "Martingale representation theorem".
| Predicate | Object |
|---|---|
| appliesTo | continuous martingales ⓘ |
| appliesTo | martingales adapted to the Brownian filtration ⓘ |
| appliesTo | square-integrable martingales ⓘ |
| assumes | completeness of probability space ⓘ |
| assumes | probability space with filtration ⓘ |
| assumes | right-continuous filtration ⓘ |
| assumes | usual conditions on filtration ⓘ |
| conclusion |
Brownian motion
ⓘ
surface form:
Brownian motion is a fundamental martingale for its natural filtration
|
| conclusion | every square-integrable martingale can be represented as a stochastic integral ⓘ |
| conclusion | martingales are generated by a fundamental martingale ⓘ |
| dealsWith | Brownian motion ⓘ |
| dealsWith | adapted processes ⓘ |
| dealsWith | filtrations ⓘ |
| dealsWith | martingales ⓘ |
| dealsWith | stochastic integrals ⓘ |
| field | probability theory ⓘ |
| field | stochastic analysis ⓘ |
| field | stochastic calculus ⓘ |
| generalizationOf | representation of martingales in Brownian filtration ⓘ |
| hasVariant | martingale representation for Lévy processes ⓘ |
| hasVariant | martingale representation for Poisson random measures ⓘ |
| hasVariant | martingale representation in general semimartingale setting ⓘ |
| implies | any L2-martingale is an Itô integral with respect to Brownian motion ⓘ |
| implies | uniqueness of integrand up to indistinguishability ⓘ |
| importance | central in theory of stochastic integration ⓘ |
| importance | fundamental structural result for martingales ⓘ |
| importance | key tool in continuous-time finance ⓘ |
| instanceOf | theorem in stochastic calculus ⓘ |
| relatedTo | Brownian filtration ⓘ |
| relatedTo | Clark–Ocone formula ⓘ |
| relatedTo |
Doob–Meyer decomposition
ⓘ
surface form:
Doob–Meyer decomposition theorem
|
| relatedTo |
Itô calculus
ⓘ
surface form:
Itô integral
|
| relatedTo |
Itô’s lemma
ⓘ
surface form:
Itô's lemma
|
| representationWithRespectTo | Brownian motion ⓘ |
| representationWithRespectTo | fundamental martingale ⓘ |
| requires | existence of stochastic integral with respect to Brownian motion ⓘ |
| requires | square-integrability of the martingale ⓘ |
| typicalFormulation | every L2-martingale adapted to the Brownian filtration is an Itô integral of a predictable process ⓘ |
| usedIn | Girsanov theorem applications ⓘ |
| usedIn | backward stochastic differential equations ⓘ |
| usedIn | completeness of financial markets ⓘ |
| usedIn | derivation of Black–Scholes formula ⓘ |
| usedIn | hedging theory ⓘ |
| usedIn | mathematical finance ⓘ |
| usedIn | stochastic control ⓘ |