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.…
References
SHOWING 1-10 OF 29 REFERENCES
Rough differential equations containing path-dependent bounded variation terms
- Mathematics
- 2016
We consider rough differential equations whose coefficients contain path-dependent bounded variation terms and prove the existence of solutions. These equations include classical path-dependent SDEs…
Delay equations driven by rough paths
- Mathematics
- 2007
In this article, we illustrate the flexibility of the algebraic integration formalism introduced in M. Gubinelli, J. Funct. Anal. 216 , 86-140, 2004, Math. Review 2005k:60169 , by establishing an…
Differential Equations Driven by Rough Paths: An Approach via Discrete Approximation
- Mathematics
- 2007
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…
Wong-Zakai approximation of solutions to reflecting stochastic differential equations on domains in Euclidean spaces II
- Mathematics
- 2014
The strong convergence of Wong-Zakai approximations of the solution to the reflecting stochastic differential equations was studied in [2]. We continue the study and prove the strong convergence…
Stochastic differential equations with reflecting boundary condition in convex regions
- Mathematics
- 1979
A. V. Skorohod [4] considered a stochastic differential equation for a reflecting diffusion process on 5 = [0, oo) (see also McKean [2] [3]). This is the simplest case among stochastic differential…
PARACONTROLLED DISTRIBUTIONS AND SINGULAR PDES
- MathematicsForum of Mathematics, Pi
- 2015
We introduce an approach to study certain singular partial differential equations (PDEs) which is based on techniques from paradifferential calculus and on ideas from the theory of controlled rough…
Differential Equations Driven by Π-Rough Paths
- MathematicsProceedings of the Edinburgh Mathematical Society
- 2016
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…
A priori estimates for rough PDEs with application to rough conservation laws
- MathematicsJournal of Functional Analysis
- 2019