Integration of Paths--A Faithful Representation of Paths by Noncommutative Formal Power Series
From MaRDI portal
Publication:3276723
DOI10.2307/1993193zbMath0097.25803OpenAlexW3146797348MaRDI QIDQ3276723
Publication date: 1959
Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.2307/1993193
Related Items (52)
Embedding and learning with signatures ⋮ Iterated path integrals and generalized paths ⋮ Developing the Path Signature Methodology and Its Application to Landmark- Based Human Action Recognition ⋮ A new functional expansion for nonlinear systems ⋮ Perturbed linear rough differential equations ⋮ Uniqueness of signature for simple curves ⋮ The moving-frame method for the iterated-integrals signature: orthogonal invariants ⋮ Spectral analysis of word statistics ⋮ Adapted topologies and higher rank signatures ⋮ Rough paths and SPDE ⋮ Weighted signature kernels ⋮ Signatures, Lipschitz-Free Spaces, and Paths of Persistence Diagrams ⋮ Topologies on unparameterised path space ⋮ Non-degeneracy of stochastic line integrals ⋮ Convex hulls of curves: volumes and signatures ⋮ Feature engineering with regularity structures ⋮ Signature cumulants, ordered partitions, and independence of stochastic processes ⋮ Iterated Integrals and Population Time Series Analysis ⋮ Toric geometry of path signature varieties ⋮ Algebras of Iterated Path Integrals and Fundamental Groups ⋮ On a Chen-Fliess approximation for diffusion functionals ⋮ VARIETIES OF SIGNATURE TENSORS ⋮ Learning with Signatures ⋮ Algebraic renormalisation of regularity structures ⋮ Volterra equations driven by rough signals ⋮ Hyperbolic development and inversion of signature ⋮ Asymptotic expansion of holonomy ⋮ On the holonomic equivalence of two curves ⋮ On Gauss-Green theorem and boundaries of a class of Hölder domains ⋮ Uniqueness for the signature of a path of bounded variation and the reduced path group ⋮ On \((p,q)\)-rough paths ⋮ Iterated path integrals ⋮ On discrete loop signatures and Markov loops topology ⋮ The uniqueness of signature problem in the non-Markov setting ⋮ On the signature and cubature of the fractional Brownian motion for \(H > \frac{1}{2}\) ⋮ Algebraic paths ⋮ A quasi-sure non-degeneracy property for the Brownian rough path ⋮ Iterated derivatives of the output of a nonlinear dynamic system and Faà di Bruno formula. ⋮ Yet another introduction to rough paths ⋮ Functional linear regression with truncated signatures ⋮ Space of signatures as inverse limits of Carnot groups ⋮ The rough Veronese variety ⋮ Eigenvalues of fourth order Sturm-Liouville problems using Fliess series ⋮ Fonctionnelles causales non linéaires et indéterminées non commutatives ⋮ Generalized holonomies ⋮ A new definition of rough paths on manifolds ⋮ Implementation of the algorithm for constructing homogeneous approximations of nonlinear control systems ⋮ Time-optimal control problem for a special class of control systems: optimal controls and approximation in the sense of time optimality ⋮ Fliess series approach to the computation of the eigenvalues of fourth-order Sturm-Liouville problems ⋮ Quasi-sure non-self-intersection for rough differential equations driven by fractional Brownian motion ⋮ The signature of a rough path: uniqueness ⋮ Algebraization of iterated integration along paths
This page was built for publication: Integration of Paths--A Faithful Representation of Paths by Noncommutative Formal Power Series