Rough differential equations with path-dependent coefficients

TL;DR

This paper proves the existence of solutions for path-dependent rough differential equations with non-anticipative coefficients, using regularity conditions based on horizontal and vertical derivatives.

Contribution

It introduces a framework for solving path-dependent rough differential equations with new regularity assumptions on coefficients.

Findings

Existence of solutions established for a class of path-dependent rough differential equations.

Regularity conditions are formulated via horizontal and vertical derivatives.

The approach extends classical rough differential equations to path-dependent cases.

Abstract

We establish the existence of solutions to path-dependent rough differential equations with non-anticipative coefficients. Regularity assumptions on the coefficients are formulated in terms of horizontal and vertical derivatives.