Itô calculus

E9112
branch of mathematics stochastic analysis stochastic calculus

Itô calculus is a branch of stochastic analysis that extends classical calculus to functions of stochastic processes, particularly Brownian motion, enabling rigorous treatment of stochastic differential equations.

Jump to: Surface forms Statements Referenced by

Observed surface forms (2)

Surface form Occurrences
Itô integral 4
Ito calculus 1

Statements (49)

Predicate Object
instanceOf branch of mathematics ⓘ
stochastic analysis ⓘ
stochastic calculus ⓘ
appliesTo Brownian motion ⓘ
Itô processes ⓘ
stochastic processes ⓘ
coreConcept Itô calculus self-linksurface differs ⓘ
surface form: Itô integral

Itô’s lemma ⓘ
adapted process ⓘ
filtration ⓘ
local martingale ⓘ
martingale ⓘ
predictable process ⓘ
quadratic variation ⓘ
stochastic differential equation ⓘ
stopping time ⓘ
coreObject Brownian motion ⓘ
semimartingales ⓘ
developedBy Kiyoshi Itô ⓘ
distinguishesFrom Stratonovich calculus ⓘ
enables martingale representation theorems ⓘ
rigorous definition of stochastic integrals ⓘ
solution of stochastic differential equations ⓘ
extends classical calculus ⓘ
feature martingale property of Itô integral ⓘ
non-anticipative integrands ⓘ
non-classical chain rule ⓘ
presence of quadratic variation term ⓘ
field probability theory ⓘ
stochastic processes ⓘ
historicalDevelopment mid 20th century ⓘ
namedAfter Kiyoshi Itô ⓘ
relatedConcept Doob–Meyer decomposition ⓘ
Feynman–Kac formula ⓘ
Girsanov theorem ⓘ
surface form: Girsanov’s theorem

stochastic exponential ⓘ
usedIn Black–Scholes model ⓘ
filtering theory ⓘ
interest rate modeling ⓘ
mathematical finance ⓘ
neuroscience modeling ⓘ
option pricing theory ⓘ
population dynamics ⓘ
quantitative risk management ⓘ
statistical physics ⓘ
stochastic control ⓘ
uses Lebesgue integration ⓘ
measure theory ⓘ
probability measure ⓘ

Referenced by (11)

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

Itô calculus → coreConcept → Itô calculus self-linksurface differs ⓘ
this entity surface form: Itô integral
this entity surface form: Itô integral
Kiyoshi Itô → knownFor → Itô calculus ⓘ
Kiyoshi Itô → notableConcept → Itô calculus ⓘ
subject surface form: Martingale representation theorem
this entity surface form: Itô integral
Itô’s lemma → relatesTo → Itô calculus ⓘ
this entity surface form: Itô integral
Itô processes → usedIn → Itô calculus ⓘ
subject surface form: Itô process
Black–Scholes model → uses → Itô calculus ⓘ
this entity surface form: Ito calculus
Feynman–Kac formula → uses → Itô calculus ⓘ
Girsanov theorem → uses → Itô calculus ⓘ