Universality of Signature Kernels Stochastic Analysis Tree-Reduced Length Is Unbounded on Open Sets Stochastic Analysis Signature as Solution of a CDE Stochastic Analysis Lusin Continuity of Response Map Stochastic Analysis Signature Determines Tree-Like Class Stochastic Analysis Unbiased MMD Estimator Stochastic Analysis Signature Universal Approximation Stochastic Analysis Local Error of the Log-ODE Method Stochastic Analysis