Develops path signature theory with Geometricity-Defect Theorem and Hopf Square, then shows finite-dimensional linear closures for truncated expected signatures of affine/exponential Hawkes processes after state augmentation.
and Hairer, Martin , title =
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A General Theory of Paths: Signatures, Jump Lifts, and Expected Signatures of Self-Exciting Processes
Develops path signature theory with Geometricity-Defect Theorem and Hopf Square, then shows finite-dimensional linear closures for truncated expected signatures of affine/exponential Hawkes processes after state augmentation.