The associativity rule in pathwise functional It\^o calculus

TL;DR

This paper proves the associativity property of the pathwise Itô integral in a functional setting, enabling more intuitive calculations of Itô differentials for continuous integrators.

Contribution

It establishes the associativity property of the pathwise Itô integral in a functional framework, a novel result in stochastic calculus.

Findings

Proves associativity of the pathwise Itô integral for continuous integrators

Provides a functional setting for pathwise Itô calculus

Enhances understanding of Itô differential computations

Abstract

In this paper we establish the associativity property of the pathwise It\^o integral in a functional setting for continuous integrators. Here, associativity refers to the computation of the It\^o differential of an It\^o integral, by means of the intuitive cancellation of the It\^o differential and integral signs.