New directions in rough path theory. Abstracts from the workshop held December 6--12, 2020 (online meeting)

DOI10.4171/OWR/2020/40zbMath1473.00046OpenAlexW3200056377MaRDI QIDQ2232323

No author found.

Publication date: 5 October 2021

Published in: Oberwolfach Reports (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4171/owr/2020/40

Mathematics Subject Classification ID

General nonlinear regression (62J02) Learning and adaptive systems in artificial intelligence (68T05) Proceedings of conferences of miscellaneous specific interest (00B25) Proceedings, conferences, collections, etc. pertaining to probability theory (60-06) Collections of abstracts of lectures (00B05) Feynman integrals and graphs; applications of algebraic topology and algebraic geometry (81Q30) Homogenization applied to problems in fluid mechanics (76M50) Machine vision and scene understanding (68T45) Stochastic analysis (60Hxx) Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.) (13P25)

Uses Software

• signature-invariants

Cites Work

• An Algebraic Theory of Integration Methods
• On the exponential solution of differential equations for a linear operator
• A regularity structure for rough volatility
• Fluid flow dynamics under location uncertainty
• Quantum stochastic processes
• A course on rough paths. With an introduction to regularity structures
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Existence and uniqueness for stochastic 2D Euler flows with bounded vorticity
• Deformations of shuffles and quasi-shuffles
• Robust filtering: correlated noise and multidimensional observation
• A Lévy area between Brownian motion and rough paths with applications to robust nonlinear filtering and rough partial differential equations
• A theory of regularity structures
• Reflected rough differential equations
• Hyperbolic development and inversion of signature
• Quasi-shuffle products revisited
• Two interacting Hopf algebras of trees: a Hopf-algebraic approach to composition and substitution of B-series.
• A non-vanishing property for the signature of a path
• On the existence of SLE trace: finite energy drivers and non-constant \(\kappa \)
• Super-multiplicativity and a lower bound for the decay of the signature of a path of finite length
• Data assimilation for a quasi-geostrophic model with circulation-preserving stochastic transport noise
• Time-warping invariants of multidimensional time series
• Ramification of rough paths
• Curvilinear integrals along enriched paths
• A variation embedding theorem and applications
• Differential equations driven by rough paths. Ecole d'Eté de Probabilités de Saint-Flour XXXIV -- 2004. Lectures given at the 34th probability summer school, July 6--24, 2004.
• On the algebra of quasi-shuffles.
• Rough differential equations driven by signals in Besov spaces
• Uniqueness for the signature of a path of bounded variation and the reduced path group
• A non-commutative sewing lemma
• Pseudo-additive measures and integrals
• Quantum probability for probabilists
• Differential equations driven by rough signals
• The Hopf algebras of decorated rooted trees. I
• Support theorem for a singular SPDE: the case of gPAM
• Differential equations driven by rough paths with jumps
• Canonical RDEs and general semimartingales as rough paths
• A priori estimates for rough PDEs with application to rough conservation laws
• Algebraic renormalisation of regularity structures
• Controlling rough paths
• Approximation and support theorem in Hölder norm for parabolic stochastic partial differential equations
• Algebraic structures of B-series
• Quasi-shuffle products
• Renormalization in quantum field theory and the Riemann-Hilbert problem. I: The Hopf algebra structure of graphs and the main theorem
• On Sobolev rough paths
• Yang-Mills measure on the two-dimensional torus as a random distribution
• Stochastic wave-current interaction in thermal shallow water dynamics
• Hairer's reconstruction theorem without regularity structures
• Paracontrolled calculus and regularity structures I.
• An energy method for rough partial differential equations
• Solving mean field rough differential equations
• A stochastic sewing lemma and applications
• A Littlewood-Paley description of modelled distributions
• Iterated-sums signature, quasisymmetric functions and time series analysis
• Signatures of paths transformed by polynomial maps
• Geometric versus non-geometric rough paths
• Rough evolution equations
• Generalized real analysis and its applications
• One-dimensional reflected rough differential equations
• Hörmander's theorem for semilinear SPDEs
• Multiscale systems, homogenization, and rough paths
• A rough path perspective on renormalization
• Invariants of multidimensional time series based on their iterated-integral signature
• On the relation between ordinary and stochastic differential equations
• The reconstruction theorem in Besov spaces
• On the Navier-Stokes equation perturbed by rough transport noise
• Renormalising SPDEs in regularity structures
• SDEs with constraints driven by processes with bounded p-variation
• PARACONTROLLED DISTRIBUTIONS AND SINGULAR PDES
• Lie Theory for Quasi-Shuffle Bialgebras
• Adapted Probability Distributions
• Multidimensional Stochastic Processes as Rough Paths
• On the Lie enveloping algebra of a pre-Lie algebra
• Stochastic backscatter of turbulence energy and scalar variance by random subgrid-scale fluxes
• A dynamic subgrid-scale eddy viscosity model
• Subgrid-scale backscatter in turbulent and transitional flows
• Stochastic backscatter in large-eddy simulations of boundary layers
• On the solution of linear differential equations in Lie groups
• Turbulent Flows
• A rough calculus approach to level sets in the Heisenberg group
• Dual Pricing of American Options by Wiener Chaos Expansion
• On a Stochastic Approach to Eddy Viscosity Models for Turbulent Flows
• Unbounded rough drivers
• Stochastic partial differential equations: a rough paths view on weak solutions via Feynman–Kac
• Numerically Modeling Stochastic Lie Transport in Fluid Dynamics
• VARIETIES OF SIGNATURE TENSORS
• Kernels for sequentially ordered data
• ON THE REGULARITY OF SLE TRACE
• Rough path metrics on a Besov–Nikolskii-type scale
• A mathematical framework for stochastic climate models
• Pricing American options by exercise rate optimization
• Space-time paraproducts for paracontrolled calculus, 3d-PAM and multiplicative Burgers equations
• HIGH ORDER PARACONTROLLED CALCULUS
• Quasi‐shuffle algebras and renormalisation of rough differential equations
• Optimal Execution with Rough Path Signatures
• A Particle Filter for Stochastic Advection by Lie Transport: A Case Study for the Damped and Forced Incompressible Two-Dimensional Euler Equation
• Characterization of nonlinear Besov spaces
• Exponentiation of conditional expectations under stochastic volatility
• Tail asymptotics of the Brownian signature
• Functional Itô calculus
• Cumulants, free cumulants and half-shuffles
• Variational principles for stochastic fluid dynamics
• Deep optimal stopping