Truncated Signature Information for Mixed Fractional Brownian Paths

Abstract

We study finite expected-signature information for mixed-fBm paths with Hurst indices above $1/4$. Up to level three, the only parameter-dependent expected features are the variance transform $q_{\theta }$ and the time-ordered transform $R_{\theta }$. We prove the scale tradeoff $2K$ level-two scales versus $K$ selected level-two/three scales, together with separation and local inverse bounds.