Rough paths and Hopf algebras

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Different notions of rough paths, such as geometric, branched, and multi-index rough paths, can be systematically understood and related through their corresponding commutative connected graded Hopf algebras. Novelty: ClaimNovelty.SYNTHESIS. Consensus alignment: ConsensusAlignment.NEUTRAL.

Dominique Manchon

doi:10.3934/jcd.2024032

September 14, 2024Journal of Computational DynamicsOpen Access

Rough paths and Hopf algebras

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Abstract

Any commutative connected graded Hopf algebra gives rise to a specific notion of rough path. This article provides a review of the different Hopf algebras, providing the various kinds of rough paths which have appeared in recent literature: geometric and quasi-geometric rough paths, branched and planarly branched rough paths, and multi-index rough paths. Relations between all these variants are also described.

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Dominique Manchon (2024) studied this question.

synapsesocial.com/papers/6aaa640a8ec1380b61f28ff8 https://doi.org/10.3934/jcd.2024032

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Rough paths and Hopf algebras

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