One-dimensional reflected rough differential equations

Aurélien Deya, Massimiliano Gubinelli, Martina Hofmanová and Samy Tindel

Stochastic Processes and their Applications, 2019, vol. 129, issue 9, 3261-3281

Abstract: 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. The whole difficulty of the problem (at least as far as uniqueness is concerned) lies in the non-continuity of the Skorohod map with respect to the topologies under consideration in the rough case. Our argument to overcome this obstacle is inspired by some ideas we introduced in a previous work dealing with rough kinetic PDEs arXiv:1604.00437.

Date: 2019
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DOI: 10.1016/j.spa.2018.09.007

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