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.
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