Title: Finiteness of radius of convergence for the logarithmic signature
Speaker: Xi Geng
Speaker Info: University of Melbourne
Brief Description:
Special Note:
Abstract:
It was conjectured by T. Lyons and N. Sidorova in 2006 that the logarithmic signature of a BV path always has finite radius of convergence unless the path is a line segment. Such a property is closely related to the study of rough differential equations from the Lie-algebraic perspective. In their original paper, the conjecture was confirmed for two special classes of paths: piecewise linear paths and one-monotone paths. In this talk, We discuss some recent progress on this problem in both probabilistic and deterministic settings. The core of the main strategy lies in understanding the dynamics of path developments onto suitably chosen Lie groups. We also discuss how such a geometric method can be used to study other problems related to the signature transform. This talk is based on previous and ongoing joint works with Horatio Boedihardjo and Sheng Wang.Date: Thursday, May 18, 2023