Triple

T12282683
Position Surface form Disambiguated ID Type / Status
Subject Malliavin calculus E292751 entity
Predicate keyConcept P531 FINISHED
Object Skorokhod integral
The Skorokhod integral is a stochastic integral extending the Itô integral to non-adapted processes, playing a central role in Malliavin calculus and anticipating stochastic analysis.
E973502 NE FINISHED

How this triple was built (4 steps)

Every LLM step that produced this triple, in pipeline order — named-entity classification, the disambiguation choices (the exact options shown, with the pick highlighted), and the generated description. The batch + timestamp of each is in the Provenance table below.

NER Named-entity recognition gpt-5-mini
Instruction
Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).
Input
Phrase: Skorokhod integral | Statement: [Malliavin calculus, keyConcept, Skorokhod integral]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Skorokhod integral
Context triple: [Malliavin calculus, keyConcept, Skorokhod integral]
  • A. Itô integral
    The Itô integral is a fundamental stochastic integral used in probability theory and mathematical finance to rigorously define integration with respect to Brownian motion and more general semimartingales.
  • B. Stratonovich integral
    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.
  • C. 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.
  • D. 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.
  • E. Itô isometry
    Itô isometry is a fundamental result in stochastic calculus that relates the L² norm of a stochastic integral with respect to Brownian motion to the L² norm of its integrand, enabling rigorous analysis of stochastic processes.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg Description generation gpt-5.1
Instruction
Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Skorokhod integral
Triple: [Malliavin calculus, keyConcept, Skorokhod integral]
Generated description
The Skorokhod integral is a stochastic integral extending the Itô integral to non-adapted processes, playing a central role in Malliavin calculus and anticipating stochastic analysis.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Skorokhod integral
Target entity description: The Skorokhod integral is a stochastic integral extending the Itô integral to non-adapted processes, playing a central role in Malliavin calculus and anticipating stochastic analysis.
  • A. Itô integral
    The Itô integral is a fundamental stochastic integral used in probability theory and mathematical finance to rigorously define integration with respect to Brownian motion and more general semimartingales.
  • B. Stratonovich integral
    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.
  • C. 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.
  • D. 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.
  • E. Itô isometry
    Itô isometry is a fundamental result in stochastic calculus that relates the L² norm of a stochastic integral with respect to Brownian motion to the L² norm of its integrand, enabling rigorous analysis of stochastic processes.
  • F. None of above. chosen

Provenance (5 batches)

The batch behind each pipeline step, in order, with when it ran. Timestamps are batch-level — stages were processed in waves, so the object chain (NER → NED1 → NEDg → NED2) reads in order, but predicate / elicitation batches can sit in a different wave.

Step Stage Batch ID Status When
creating Elicitation batch_69d6ab690ad081908c0ed3870ec82d53 completed April 8, 2026, 7:24 p.m.
NER Named-entity recognition batch_69d91cf2b09c81908a11581d33f65be0 completed April 10, 2026, 3:53 p.m.
NED1 Entity disambiguation (via context triple) batch_69f61e70dec8819098199fbb54d888c1 completed May 2, 2026, 3:55 p.m.
NEDg Description generation batch_69f61f5bc1fc8190af9d74acc307ebe1 completed May 2, 2026, 3:59 p.m.
NED2 Entity disambiguation (via description) batch_69f62045b20c819083c755fbe99a9a7f completed May 2, 2026, 4:03 p.m.
Created at: April 8, 2026, 9:52 p.m.