Rough path theory and stochastic calculus

TL;DR

This paper surveys rough path theory, a deterministic framework that extends stochastic calculus by incorporating iterated integrals, highlighting its probabilistic aspects and connections to stochastic differential equations.

Contribution

It provides a comprehensive overview of rough path theory, emphasizing its probabilistic features and its relation to classical stochastic calculus.

Findings

Highlights the deterministic nature of rough path theory.

Connects rough path theory with stochastic differential equations.

Emphasizes probabilistic aspects of rough path analysis.

Abstract

T. Lyons' rough path theory is something like a deterministic version of K. Ito's theory of stochastic differential equations, combined with ideas from K. T. Chen's theory of iterated path integrals. In this article we survey rough path theory, in particular, its probabilistic aspects.