Integration of paths, geometric invariants and a generalized Baker-Hausdorff formula

From MaRDI portal
Publication:768531

DOI10.2307/1969671zbMath0077.25301OpenAlexW2321579306MaRDI QIDQ768531

Kuo-Tsai Chen

Publication date: 1957

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: http://www.jstor.org/pss/1969671




Related Items

Necessary conditions for local controllability of a particular class of systems with two scalar controlsSeries expansions for analytic systems linear in controlStochastic differential equations driven by loops in Carnot groups.ASCENDING CHAIN CONDITIONS IN FREE BAXTER ALGEBRASStochastic Differential Equations Driven by LoopsVers une notion de dérivation fonctionnelle causale. (Towards a notion of causal functional derivatives)Time-warping invariants of multidimensional time seriesOn the Complexity of Isomorphism Problems for Tensors, Groups, and Polynomials I: Tensor Isomorphism-CompletenessUnnamed ItemMonte Carlo construction of cubature on Wiener spaceThe Campbell-Baker-Hausdorff-Dynkin formula and solutions of differential equationsTropical Time Series, Iterated-Sums Signatures, and Quasisymmetric FunctionsOn the Number of Turns in Reduced Random Lattice PathsFrom random walks to rough pathsFlows and stochastic Taylor series in Itô calculusAn algebraic criterion for the onset of chaos in nonlinear dynamical systemsTheory of Koszul operads and homology of Poisson algebrasA signed measure on rough paths associated to a PDE of high order: results and conjecturesAlgebraic and multiple integral identitiesSmooth density for some nilpotent rough differential equationsStratonovich's signatures of Brownian motion determine Brownian sample pathsFormal power series, operator calculus, and duality on Lie algebrasLie algebraic representation results for nonstationary evolution operatorsSome algebraic aspects of the center problem for ordinary differential equationsVariational principles for fluid dynamics on rough pathsExplicit solutions of the \({\mathfrak{a}_1}\)-type Lie-Scheffers system and a general Riccati equationWord combinatorics for stochastic differential equations: splitting integratorsPerturbed linear rough differential equationsUniqueness of signature for simple curvesSignature-Based Models: Theory and CalibrationA structure theorem for streamed informationHOPF ALGEBRAS IN DYNAMICAL SYSTEMS THEORYCumulants as iterated integralsOn expansions for nonlinear systems error estimates and convergence issuesOptimal stopping with signaturesRough paths and SPDELocal small time controllability and attainability of a set for nonlinear control systemPlanarly branched rough paths and rough differential equations on homogeneous spacesIterated Integrals and Population Time Series AnalysisSignatures of paths transformed by polynomial mapsOn the Classification of Operator IdentitiesTaylor expansions of groups and filtered-formalitySolving Rough Differential Equations with the Theory of Regularity StructuresMalliavin calculus and rough pathsNon-explosion criteria for rough differential equations driven by unbounded vector fieldsThe early days of geometric nonlinear controlToric geometry of path signature varietiesA combinatorial method for calculating the moments of Lévy areaMichel Fliess and non-commutative formal power series†Algebras of Iterated Path Integrals and Fundamental GroupsOn a Chen-Fliess approximation for diffusion functionalsBaxter algebras and shuffle productsLearning Paths from Signature TensorsRecursion formulas for the Lie integralVARIETIES OF SIGNATURE TENSORSA brief and personal history of stochastic partial differential equationsKONTSEVICH'S UNIVERSAL FORMULA FOR DEFORMATION QUANTIZATION AND THE CAMPBELL–BAKER–HAUSDORFF FORMULAAlgebraic renormalisation of regularity structuresA quadratic identity in the shuffle algebra and an alternative proof for de Bruijn's formulaBrownian Chen series and Atiyah-Singer theoremHyperbolic development and inversion of signatureFormal paths, iterated integrals and the center problem for ordinary differential equationsMultiple integrals and expansion of solutions of differential equations driven by rough paths and by fractional Brownian motionsComputation of multiple Lie derivatives by algorithmic differentiationOn Gauss-Green theorem and boundaries of a class of Hölder domainsDensities for rough differential equations under Hörmander's conditionStochastic differential equations driven by processes generated by divergence form operators I: a Wong-Zakai theoremConvergence of the exponential Lie seriesLie algebras associated with the exponential solutions of nonautonomous linear differential equationsProbabilistic methods for semilinear partial differential equations. Applications to financeMixable shuffles, quasi-shuffles and Hopf algebras.Differential equations driven by Gaussian signalsInfinite-dimensional polynomial processesBaxter algebras and Hopf algebrasShadow Forms of Brasselet-Goresky-MacPhersonFirst integrals for nonlinear dispersive equationsMultiple zeta valuesIterated path integralsCommutative matching Rota-Baxter operators, shuffle products with decorations and matching Zinbiel algebrasOn the signature and cubature of the fractional Brownian motion for \(H > \frac{1}{2}\)On the definition of a solution to a rough differential equationStabilité d'un type élémentaire d'équations diffé rentielles stochastiques à bruits vectorieslAlgebraic pathsA Technique for Studying Strong and Weak Local Errors of Splitting Stochastic IntegratorsProperties of free Baxter algebrasAn isomorphism between branched and geometric rough pathsYet another introduction to rough pathsConstructing general rough differential equations through flow approximationsA group-theoretical approach to conditionally free cumulantsStructure Theorems of Mixable Shuffle AlgebrasFonctionnelles causales non linéaires et indéterminées non commutativesGeneralized holonomiesInvariants of multidimensional time series based on their iterated-integral signatureNumerical evaluation of the Evans function by Magnus integrationA new definition of rough paths on manifoldsQuasi-shuffle algebras in non-commutative stochastic calculusThe algebra and combinatorics of shuffles and multiple zeta valuesPfaffian and Hafnian identities in shuffle algebrasSome multi-set inclusions associated with shuffle convolutions and multiple zeta valuesThe signature of a rough path: uniqueness