Signature of Time Reversal Stochastic Analysis Signature as Solution of a CDE Stochastic Analysis Injectivity For Time-Augmented Paths Stochastic Analysis Local Existence and Explosion for Lip-alpha RDEs Stochastic Analysis Sufficient Condition for Signature Membership Stochastic Analysis Global Error of Euler Scheme Stochastic Analysis Unique Global Solutions under Lipschitz Hypotheses Stochastic Analysis MMD Metrizes Weak Convergence Stochastic Analysis