Local Error of the Log-ODE Method Stochastic Analysis Linear Independence of Distinct Signatures Stochastic Analysis Characterisation of Cauchy Sequences in the Signature Pre-RKHS Stochastic Analysis Representer Theorem for Signature Kernels Stochastic Analysis Integral Equation for Weighted Signature Kernels Stochastic Analysis No Explosion under Linear Growth Stochastic Analysis Extension Theorem (rough paths) Stochastic Analysis Factorial Decay Stochastic Analysis