Stratonovich integral
E295051
The Stratonovich integral is a formulation of stochastic integration that preserves the classical chain rule of calculus and is widely used in physics and engineering for modeling systems with noise.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Stratonovich integral canonical | 2 |
| Stratonovich–Fisk integral | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T2716842 — 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: Stratonovich integral Context triple: [Itô’s lemma, relatesTo, Stratonovich integral]
-
A.
Riemann–Stieltjes integral
The Riemann–Stieltjes integral is a generalization of the Riemann integral in which integration is taken with respect to a function of bounded variation rather than just the identity function, allowing more flexible treatment of sums and distributions.
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B.
Itô 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.
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C.
Henstock–Kurzweil integral
The Henstock–Kurzweil integral is a highly general integration theory that extends and refines the Riemann integral, capable of integrating a broader class of functions while retaining many of the intuitive properties of Riemann integration.
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D.
Itô’s lemma
Itô’s lemma is a fundamental result in stochastic calculus that generalizes the chain rule to functions of stochastic processes, especially Brownian motion.
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E.
Itô processes
Itô processes are a class of stochastic processes, typically modeled as solutions to stochastic differential equations, that form the fundamental objects of study in Itô calculus and modern stochastic analysis.
- 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: Stratonovich integral Target entity description: The Stratonovich integral is a formulation of stochastic integration that preserves the classical chain rule of calculus and is widely used in physics and engineering for modeling systems with noise.
-
A.
Riemann–Stieltjes integral
The Riemann–Stieltjes integral is a generalization of the Riemann integral in which integration is taken with respect to a function of bounded variation rather than just the identity function, allowing more flexible treatment of sums and distributions.
-
B.
Itô 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.
-
C.
Henstock–Kurzweil integral
The Henstock–Kurzweil integral is a highly general integration theory that extends and refines the Riemann integral, capable of integrating a broader class of functions while retaining many of the intuitive properties of Riemann integration.
-
D.
Itô’s lemma
Itô’s lemma is a fundamental result in stochastic calculus that generalizes the chain rule to functions of stochastic processes, especially Brownian motion.
-
E.
Itô processes
Itô processes are a class of stochastic processes, typically modeled as solutions to stochastic differential equations, that form the fundamental objects of study in Itô calculus and modern stochastic analysis.
- F. None of above. chosen
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical concept
ⓘ
object in stochastic calculus ⓘ stochastic integral ⓘ |
| advantageOverItôIntegral |
invariant under smooth coordinate changes
ⓘ
preserves ordinary chain rule ⓘ |
| assumes | non-anticipative integrands ⓘ |
| comparedTo | Itô integral ⓘ |
| contrastWith |
Skorokhod integral
ⓘ
pathwise Riemann–Stieltjes integral ⓘ |
| definitionInvolves |
limit in probability of stochastic Riemann sums
ⓘ
midpoint Riemann sums ⓘ |
| disadvantageComparedToItôIntegral |
less convenient for martingale methods
ⓘ
less natural for financial mathematics modeling ⓘ |
| domain |
continuous semimartingales
ⓘ
semimartingales ⓘ |
| field |
mathematical physics
ⓘ
probability theory ⓘ stochastic calculus ⓘ |
| hasAlternativeName |
Stratonovich integral
ⓘ
surface form:
Stratonovich–Fisk integral
|
| hasProperty |
agrees with classical calculus in deterministic limit
ⓘ
can be expressed in terms of Itô integral plus correction term ⓘ coincides with Riemann–Stieltjes integral for smooth paths ⓘ coordinate-invariant under smooth transformations ⓘ often preferred in physical modeling ⓘ time-symmetric definition ⓘ |
| introducedIn | 20th century ⓘ |
| mathematicalNature | limit of symmetric stochastic sums ⓘ |
| namedAfter | Ruslan Stratonovich NERFINISHED ⓘ |
| relatedConcept |
Itô calculus
ⓘ
Itô–Stratonovich conversion formula ⓘ stochastic differential equation ⓘ |
| requires | quadratic variation of integrator ⓘ |
| satisfies |
classical chain rule of calculus
ⓘ
ordinary change-of-variables formula ⓘ |
| typicalIntegrand | adapted stochastic process ⓘ |
| typicalIntegrator |
Brownian motion
ⓘ
Wiener process ⓘ |
| usedFor |
modeling Langevin-type equations
ⓘ
modeling systems with continuous noise ⓘ stochastic modeling on manifolds ⓘ |
| usedIn |
control theory
ⓘ
engineering ⓘ physics ⓘ signal processing ⓘ statistical mechanics ⓘ stochastic differential equations ⓘ |
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: Stratonovich integral Description of subject: The Stratonovich integral is a formulation of stochastic integration that preserves the classical chain rule of calculus and is widely used in physics and engineering for modeling systems with noise.
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Stratonovich–Fisk integral