One-dimensional reflected rough differential equations

Aurélien Deya (1) , Massimiliano Gubinelli (2) , Martina Hofmanova (3) , Samy Tindel (4)

1 IECL - Institut Élie Cartan de Lorraine
2 Hausdorff Center for Mathematics and Institute for Numerical Simulation - University of Bonn
3 Department of Mathematics, Technical University Berlin
4 Department of mathematics Purdue University

We prove existence and uniqueness of the solution of a one-dimensional rough differential equation driven by a step-2 rough path and reflected at zero. In order to deal with the lack of control of the reflection measure the proof uses some ideas we introduced in a previous work dealing with rough kinetic PDEs [arXiv:1604.00437].

Domaines: Probabilités [math.PR]

Aurélien Deya, Massimiliano Gubinelli, Martina Hofmanova, Samy Tindel. One-dimensional reflected rough differential equations. Stochastic Processes and their Applications, 2019, 129 (1), pp.3261-3681. ⟨10.1016/j.spa.2018.09.007⟩. ⟨hal-01387724⟩