Path developments and tail asymptotics of signature for pure rough paths
Horatio Boedihardjo, Xi Geng, Nikolaos P Souris
ADVANCES IN MATHEMATICS | ACADEMIC PRESS INC ELSEVIER SCIENCE | Published : 2020
Solutions to linear controlled differential equations can be expressed in terms of global iterated path integrals along the driving path. This collection of iterated integrals encodes essentially all information about the underlying path. While upper bounds for iterated path integrals are well known, lower bounds are much less understood, and it is known only relatively recently that some types of asymptotics for the n-th order iterated integral can be used to recover some intrinsic quantitative properties of the path, such as the length for C1 paths. In the present paper, we investigate the simplest type of rough paths (the rough path analogue of line segments), and establish uniform upper ..View full abstract
Awarded by EPSRC
Awarded by NSF
HB and NS are supported by EPSRC grant EP/R008205/1. XG is supported in part by NSF grant DMS1814147. The authors wish to thank Dr Wenzhe Yang for his valuable comments and suggestions from the viewpoint of algebraic geometry.