[图书][B] A course on rough paths

PK Friz, M Hairer - 2020 - Springer
Peter K. Friz Martin Hairer With an Introduction to Regularity Structures Second Edition
Page 1 Universitext Peter K. Friz Martin Hairer A Course on Rough Paths With an …

Developing the path signature methodology and its application to landmark-based human action recognition

W Yang, T Lyons, H Ni, C Schmid, L Jin - Stochastic Analysis, Filtering …, 2022 - Springer
Landmark-based human action recognition in videos is a challenging task in computer
vision. One key step is to design a generic approach that generates discriminative features …

Path signatures for diversity in probabilistic trajectory optimisation

L Barcelos, T Lai, R Oliveira… - … Journal of Robotics …, 2024 - journals.sagepub.com
Motion planning can be cast as a trajectory optimisation problem where a cost is minimised
as a function of the trajectory being generated. In complex environments with several …

Time-warping invariants of multidimensional time series

J Diehl, K Ebrahimi-Fard, N Tapia - Acta Applicandae Mathematicae, 2020 - Springer
In data science, one is often confronted with a time series representing measurements of
some quantity of interest. Usually, in a first step, features of the time series need to be …

Learning paths from signature tensors

M Pfeffer, A Seigal, B Sturmfels - SIAM Journal on Matrix Analysis and …, 2019 - SIAM
Matrix congruence extends naturally to the setting of tensors. We apply methods from tensor
decomposition, algebraic geometry, and numerical optimization to this group action. Given a …

Smooth rough paths, their geometry and algebraic renormalization

C Bellingeri, PK Friz, S Paycha, R Preiß - Vietnam Journal of Mathematics, 2022 - Springer
We introduce the class of “smooth rough paths” and study their main properties. Working in a
smooth setting allows us to discard sewing arguments and focus on algebraic and geometric …

Rank and symmetries of signature tensors

F Galuppi, P Santarsiero - arXiv preprint arXiv:2407.20405, 2024 - arxiv.org
The signature of a path is a sequence of tensors which allows to uniquely reconstruct the
path. In this paper we propose a systematic study of basic properties of signature tensors …

The barycenter in free nilpotent Lie groups and its application to iterated-integrals signatures

M Clausel, J Diehl, R Mignot, L Schmitz, N Sugiura… - SIAM Journal on Applied …, 2024 - SIAM
We establish the well-definedness of the barycenter (in the sense of Buser and Karcher) for
every integrable measure on the free nilpotent Lie group of step (over). We provide two …

Tropical time series, iterated-sums signatures, and quasisymmetric functions

J Diehl, K Ebrahimi-Fard, N Tapia - SIAM Journal on Applied Algebra and …, 2022 - SIAM
Aiming for a systematic feature extraction from time series, we introduce the iterated-sums
signature over arbitrary commutative semirings. The case of the tropical semiring is a …

Rectifiable paths with polynomial log‐signature are straight lines

PK Friz, T Lyons, A Seigal - Bulletin of the London Mathematical …, 2024 - Wiley Online Library
The signature of a rectifiable path is a tensor series in the tensor algebra whose coefficients
are definite iterated integrals of the path. The signature characterizes the path up to a …