# Sweeping Processes Perturbed by Rough Signals

## TL;DR

This paper investigates the mathematical properties and solution methods for sweeping processes influenced by rough signals, including fractional Brownian motion, focusing on existence, uniqueness, and approximation schemes.

## Contribution

It introduces new results on the existence, uniqueness, and approximation of solutions to sweeping processes perturbed by rough signals with finite p-variation.

## Key findings

- Established existence and uniqueness of solutions.
- Developed an approximation scheme for solutions.
- Extended analysis to fractional Brownian motion with Hurst > 1/3.

## Abstract

This paper deals with the existence, the uniqueness and an approximation scheme of the solution to sweeping processes perturbed by a continuous signal of finite $p$-variation with $p\in [1,3[$. It covers pathwise stochastic noises directed by a fractional Brownian motion of Hurst parameter greater than $1/3$.