Generative Path-Law Jump-Diffusion: Sequential MMD-Gradient Flows and Generalisation Bounds in Marcus-Signature RKHS

This paper introduces a novel generative framework for synthesising forward-looking, càdlàg stochastic trajectories that are sequentially consistent with time-evolving path-law proxies, thereby incorporating anticipated structural breaks, regime shifts, and non-autonomous dynamics. By framing path synthesis as a sequential matching problem on restricted Skorokhod manifolds, we develop the \textit{Anticipatory Neural Jump-Diffusion} (ANJD) flow, a generative mechanism that effectively inverts the time-extended Marcus-sense signature. Central to this approach is the Anticipatory Variance-Normalised Signature Geometry (AVNSG), a time-evolving precision operator that performs dynamic spectral...

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