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New method characterizes expected signature kernels for Lévy rough paths

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Researchers have developed a method to characterize the expected signature kernel for Lévy rough paths, a measure of similarity for probability laws on path space. This work builds upon previous research and provides a new description for these kernels, particularly in the context of Goursat-type systems. The study details how to handle both continuous and jump processes, offering finite-dimensional truncations with error control for the latter. Additionally, the paper presents a way to derive an unbiased statistic for signature-MMD tests for conditionally Gaussian martingales, demonstrating variance reduction and increased power through computable finite-grid versions. AI

RANK_REASON The item is a research paper published on arXiv detailing mathematical methods. [lever_c_demoted from research: ic=1 ai=0.1]

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New method characterizes expected signature kernels for Lévy rough paths

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The item is a research paper published on arXiv detailing mathematical methods. [lever_c_demoted from research: ic=1 ai=0.1]
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COVERAGE [1]

  1. arXiv stat.ML TIER_1 English(EN) · Peter K. Friz, Paul P. Hager ·

    Expected Signature Kernels for Rough Paths

    arXiv:2509.07893v2 Announce Type: replace-cross Abstract: The expected signature kernel is a similarity measure of probability laws on path space and enters directly into signature maximum mean discrepancies. Building on [P. K. Friz, P. P. Hager, and N. Tapia, Forum Math. Sigma, …

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