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}
}
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17 Citations
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17 Citations

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References

SHOWING 1-10 OF 29 REFERENCES

Rough differential equations containing path-dependent bounded variation terms

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

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

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

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…

Controlling rough paths

Stochastic differential equations with reflecting boundary condition in convex regions

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

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…

Rough Volterra equations 2: Convolutional generalized integrals

Differential Equations Driven by Π-Rough Paths

  • L. Gyurkó
  • Mathematics
    Proceedings 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