Càdlàg rough differential equations with reflecting barriers

Allan, Andrew L.; Liu, Chong; Prömel, David J.

Abstract

We investigate rough differential equations with a time-dependent reflecting lower barrier, where both the driving (rough) path and the barrier itself may have jumps. Assuming the driving signals allow for Young integration, we provide existence, uniqueness and stability results. When the driving signal is a càdlàg p-rough path for p ∈ [2, 3), we establish existence to general reflected rough differential equations, as well as uniqueness in the one-dimensional case.

Citation

Allan, A. L., Liu, C., & Prömel, D. J. (2021). Càdlàg rough differential equations with reflecting barriers. Stochastic Processes and their Applications, 142, 79-104. https://doi.org/10.1016/j.spa.2021.08.004

• Journal Article Type: Article
• Acceptance Date: Aug 18, 2021
• Online Publication Date: Aug 25, 2021
• Publication Date: 2021-12
• Deposit Date: Jan 24, 2023
• Publicly Available Date: Jan 24, 2023
• Journal: Stochastic Processes and their Applications
• Print ISSN: 0304-4149
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 142
• Pages: 79-104
• DOI: https://doi.org/10.1016/j.spa.2021.08.004