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arXiv · 2408.06978

Rough Stochastic Analysis with Jumps

Andrew L. Allan·Jost Pieper
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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.

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Andrew L. Allan, Jost Pieper. 2024-08-13. Rough Stochastic Analysis with Jumps. https://arxiv.org/abs/2408.06978

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