# One-dimensional reflected rough differential equations

@article{Deya2016OnedimensionalRR, title={One-dimensional reflected rough differential equations}, author={Aur'elien Deya and Massimiliano Gubinelli and Martina Hofmanov{\'a} and Samy Tindel}, journal={Stochastic Processes and their Applications}, year={2016} }

## 17 Citations

### Rough differential equations with path-dependent coefficients

- Mathematics
- 2020

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…

### An energy method for rough partial differential equations

- MathematicsJournal of Differential Equations
- 2018

### Non-uniqueness for reflected rough differential equations

- MathematicsAnnales de l'Institut Henri Poincaré, Probabilités et Statistiques
- 2021

We give an example of a reflected diffferential equation which may have infinitely many solutions if the driving signal is rough enough (e.g. of infinite $p$-variation, for some $p>2$). For this…

### Navier-Stokes equations perturbed by a rough transport noise

- Mathematics
- 2017

We consider a Navier-Stokes equation in two and three space dimensions subject to periodic boundary conditions and perturbed by a transport type noise. The perturbation is sufficiently smooth in…

### Sweeping Processes Perturbed by Rough Signals

- Mathematics
- 2018

This paper deals with the existence and the uniqueness of the solution to sweeping processes perturbed by a continuous signal of finite p-variation with $p\in [1,3[$. It covers pathwise stochastic…

### On the Navier–Stokes equation perturbed by rough transport noise

- MathematicsJournal of Evolution Equations
- 2018

We consider the Navier–Stokes system in two and three space dimensions perturbed by transport noise and subject to periodic boundary conditions. The noise arises from perturbing the advecting…

### Penalisation techniques for one-dimensional reflected rough differential equations

- MathematicsBernoulli
- 2020

In this paper we solve real-valued rough differential equations (RDEs) reflected on an irregular boundary. The solution $Y$ is constructed as the limit of a sequence $(Y^n)_{n\in\mathbb{N}}$ of…

### Bilinear equations in Hilbert space driven by paths of low regularity

- MathematicsDiscrete & Continuous Dynamical Systems - B
- 2021

In the article, some bilinear evolution equations in Hilbert space driven by paths of low regularity are considered and solved explicitly. The driving paths are scalar-valued and continuous, and they…

### Perturbations of singular fractional SDEs

- Mathematics
- 2022

. We obtain well-posedness results for a class of ODE with a singular drift and additive fractional noise, whose right-hand-side involves some bounded variation terms depending on the solution.…

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driving path x(t) is nondifferentiable, has recently been developed by Lyons. I develop an alternative approach to this theory, using (modified) Euler approximations, and investigate its…

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Abstract This paper revisits the concept of rough paths of inhomogeneous degree of smoothness (geometric Π-rough paths in our terminology) sketched by Lyons in 1998. Although geometric Π-rough paths…

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