A regularity structure is a mathematical framework developed primarily for the study of certain types of stochastic partial differential equations (SPDEs) and singular stochastic PDEs. Introduced by Martin Hairer in his groundbreaking work on the theory of rough paths and stochastic analysis, regularity structures provide a way to analyze and solve equations that can be highly irregular or chaotic in nature, which typically arise in various fields such as physics, finance, and engineering.
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