Rough differential equations containing path-dependent bounded variation terms
arXiv:1608.03083 · doi:10.1007/s10959-024-01319-3
Abstract
We consider rough differential equations whose coefficients contain path-dependent bounded variation terms and prove the existence and a priori estimate of solutions. These equations include classical path-dependent SDEs containing running maximum processes and normal reflection terms. We apply these results to determine the topological support of the solution processes.
This version is accepted for publication in Journal of Theoretical Probability. In this version, we add new subjects related with perturbed reflected RDE. Also we rewrite many parts