Adapted topologies and higher rank signatures

DOI10.1214/22-aap1862arXiv2005.08897MaRDI QIDQ6104023

Chong Liu, Harald Oberhauser, Patric Bonnier

Publication date: 5 June 2023

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2005.08897

zbMATH Keywords

prediction processextended weak convergenceadapted functionalsadapted topologiesrobust signatures

Mathematics Subject Classification ID

General theory of stochastic processes (60G07) Signatures and data streams (60L10)

Related Items

Signatures, Lipschitz-Free Spaces, and Paths of Persistence Diagrams ⋮ Topologies on unparameterised path space ⋮ A note on the adapted weak topology in discrete time

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Dynamic generation of scenario trees
• Stochastic optimal control. The discrete time case
• Canonical RDEs and general semimartingales as rough paths
• Estimating processes in adapted Wasserstein distance
• Fundamental properties of process distances
• All adapted topologies are equal
• General rough integration, Lévy rough paths and a Lévy-Kintchine-type formula
• On a Wasserstein-type distance between solutions to stochastic differential equations
• Sequential decisions under uncertainty and the maximum theorem
• From Empirical Observations to Tree Models for Stochastic Optimization: Convergence Properties
• Multistage Stochastic Optimization
• A Distance For Multistage Stochastic Optimization Models
• The Wasserstein distance and approximation theorems
• Integration of Paths--A Faithful Representation of Paths by Noncommutative Formal Power Series
• Adapted Probability Distributions
• Multidimensional Stochastic Processes as Rough Paths
• Causal transport plans and their Monge–Kantorovich problems
• System Control and Rough Paths
• Evaluations of Risk Measures for Different Probability Measures
• Cumulants, free cumulants and half-shuffles
• Iterated Integrals and Exponential Homomorphisms^†