English

Rough Stochastic Analysis with Jumps

Probability 2026-03-30 v2

Abstract

We present a new version of the stochastic sewing lemma, capable of handling multiple discontinuous control functions. This is then used to develop a theory of rough stochastic analysis in a c\`adl\`ag setting. In particular, we define rough stochastic integration and establish solutions to rough stochastic differential equations with jump discontinuities in both sources of noise, along with an It\^o formula for stochastic controlled paths with jumps.

Keywords

Cite

@article{arxiv.2408.06978,
  title  = {Rough Stochastic Analysis with Jumps},
  author = {Andrew L. Allan and Jost Pieper},
  journal= {arXiv preprint arXiv:2408.06978},
  year   = {2026}
}

Comments

63 pages

R2 v1 2026-06-28T18:11:53.576Z