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This subtopic introduces the core ideas in rough analysis and related topics, including foundational concepts, standard methods, and the main questions used to organize the area. Typical uses include building mathematical background, framing related research problems, and supporting applications in neighboring fields where these concepts provide useful structure.
Signatures and the log-signature map. This topic studies rough analysis and related frameworks for highly irregular signals and paths beyond classical smooth stochastic calculus.
Used to define and analyze differential equations driven by rough or distributional signals.
Rough paths. This topic studies rough analysis and related frameworks for highly irregular signals and paths beyond classical smooth stochastic calculus.
Used to define and analyze differential equations driven by rough or distributional signals.
Regularity structures. This topic studies rough analysis and related frameworks for highly irregular signals and paths beyond classical smooth stochastic calculus.
Used to define and analyze differential equations driven by rough or distributional signals.
Stochastic partial differential equations and regularity structures. This topic studies rough analysis and related frameworks for highly irregular signals and paths beyond classical smooth stochastic calculus.
Used to define and analyze differential equations driven by rough or distributional signals.
Stochastic analysis, rough paths. This topic studies rough analysis and related frameworks for highly irregular signals and paths beyond classical smooth stochastic calculus.
Used to define and analyze differential equations driven by rough or distributional signals.
Algebra and geometry of rough paths. This topic studies rough analysis and related frameworks for highly irregular signals and paths beyond classical smooth stochastic calculus.
Used to define and analyze differential equations driven by rough or distributional signals.
Applications of rough paths. This topic studies rough analysis and related frameworks for highly irregular signals and paths beyond classical smooth stochastic calculus.
Used to define and analyze differential equations driven by rough or distributional signals.
None of the above. This topic studies rough analysis and related frameworks for highly irregular signals and paths beyond classical smooth stochastic calculus.
Used to define and analyze differential equations driven by rough or distributional signals.