Operads in It{\^o} calculus
Roland Friedrich
TL;DR
This paper explores the algebraic and geometric structures underlying Itô calculus, aiming to deepen understanding of its mathematical foundations.
Contribution
It introduces a novel operadic framework to analyze the algebraic and geometric aspects of Itô calculus.
Findings
Operadic structures elucidate Itô calculus properties
New algebraic relations in stochastic calculus
Geometric interpretations of stochastic integrals
Abstract
We discuss algebraic and geometric properties of the It{\^o} calculus
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Noncommutative and Quantum Gravity Theories · Black Holes and Theoretical Physics