English

Path-dependent rough differential equations

Probability 2013-09-06 v1 Classical Analysis and ODEs

Abstract

We show in this work how the machinery of C^1-approximate flows introduced in our previous work "Flows driven by rough paths", provides a very efficient tool for proving well-posedness results for path-dependent rough differential equations on flows of the form d\phi = V h(dt) + F X(dt), for smooth enough path-dependent vector fields V,F = (V_1,...,V_\ell), any Holder weak geometric p-rough path X and any a-Holder path h, with a+1/p>1.

Keywords

Cite

@article{arxiv.1309.1291,
  title  = {Path-dependent rough differential equations},
  author = {Ismael Bailleul},
  journal= {arXiv preprint arXiv:1309.1291},
  year   = {2013}
}

Comments

17 pages

R2 v1 2026-06-22T01:21:18.647Z