The Wasserstein space of stochastic processes

D Bartl, M Beiglböck, G Pammer - Journal of the European Mathematical …, 2024 - ems.press
Wasserstein distance induces a natural Riemannian structure for the probabilities on the
Euclidean space. This insight of classical transport theory is fundamental for tremendous …

General duality and dual attainment for adapted transport

D Kršek, G Pammer - arXiv preprint arXiv:2401.11958, 2024 - arxiv.org
We investigate duality and existence of dual optimizers for several adapted optimal transport
problems under minimal assumptions. This includes the causal and bicausal transport, the …

Representing General Stochastic Processes as Martingale Laws

M Beiglböck, G Pammer, S Schrott, X Zhang - arXiv preprint arXiv …, 2023 - arxiv.org
Random variables $ X^ i $, $ i= 1, 2$ are'probabilistically equivalent'if they have the same
law. Moreover, in any class of equivalent random variables it is easy to select canonical …

Bisimulation Metrics are Optimal Transport Distances, and Can be Computed Efficiently

S Calo, A Jonsson, G Neu, L Schwartz… - arXiv preprint arXiv …, 2024 - arxiv.org
We propose a new framework for formulating optimal transport distances between Markov
chains. Previously known formulations studied couplings between the entire joint distribution …

A Probabilistic View on the Adapted Wasserstein Distance

M Beiglböck, S Pflügl, S Schrott - arXiv preprint arXiv:2406.19810, 2024 - arxiv.org
Causal optimal transport and adapted Wasserstein distance have applications in different
fields from optimization to mathematical finance and machine learning. The goal of this …

Distributionally Robust Kalman Filter Fusion for Multi-sensor System

D Wang, W Li, J Lyu, Z Cao… - 2024 39th Youth …, 2024 - ieeexplore.ieee.org
The aim of this study is to develop a robust module through the integration of distributionally
robust Kalman filter with multi-sensor fusion. Leveraging the established reliability of the …

Bisimulation Metrics are Optimal Transport Distances, and Can be Computed Efficiently

SC Oliveira, A Jonsson, G Neu, L Schwartz… - The Thirty-eighth Annual … - openreview.net
We propose a new framework for formulating optimal transport distances between Markov
chains. Previously known formulations studied couplings between the entire joint distribution …