Time-reversibility and nonvanishing Levy area

TL;DR

This paper thoroughly analyzes the Levy area correction in stochastic integrals derived from time-reversible deterministic systems, revealing conditions under which the Levy area vanishes due to time-reversibility.

Contribution

It provides a complete classification of when Levy area corrections vanish, clarifying the structure of stochastic integrals from time-reversible systems.

Findings

Levy area correction vanishes only in specific classified situations.

Time-reversibility imposes strict conditions on Levy area behavior.

The structure of Levy area corrections is fully described and clarified.

Abstract

We give a complete description and clarification of the structure of the Levy area correction to Ito/Stratonovich stochastic integrals arising as limits of time-reversible deterministic dynamical systems. In particular, we show that time-reversibility forces the Levy area to vanish only in very specific situations that are easily classified.