Rough Paths and Regularity Structures
Lyons' rough paths and Hairer's regularity structures for singular SPDEs.
Rough Paths and Regularity Structures. Lyons’ rough paths and Hairer’s regularity structures for singular SPDEs.
Foundations and canonical references
The standard treatments of rough paths and regularity structures approach the subject from complementary angles. Friz, A Course on Rough Paths (2014) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to.
Open methodological questions for rough paths and regularity structures include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 2014A Course on Rough Pathsfriz-2014, hairer-2014
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