Related papers: Estimating processes in adapted Wasserstein distan…
Researchers from different areas have independently defined extensions of the usual weak convergence of laws of stochastic processes with the goal of adequately accounting for the flow of information. Natural approaches are convergence of…
A number of researchers have introduced topological structures on the set of laws of stochastic processes. A unifying goal of these authors is to strengthen the usual weak topology in order to adequately capture the temporal structure of…
The Wasserstein distance $\mathcal{W}_p$ is an important instance of an optimal transport cost. Its numerous mathematical properties as well as applications to various fields such as mathematical finance and statistics have been well…
We consider empirical measures of $\R^{d}$-valued stochastic process in finite discrete-time. We show that the adapted empirical measure introduced in the recent work \cite{backhoff2022estimating} by Backhoff et al. in compact spaces can be…
The adapted Wasserstein distance is a metric for quantifying distributional uncertainty and assessing the sensitivity of stochastic optimization problems on time series data. A computationally efficient alternative to it, is provided by the…
The adapted weak topology is an extension of the weak topology for stochastic processes designed to adequately capture properties of underlying filtrations. With the recent work of Bart--Beiglb\"ock-P. as starting point, the purpose of this…
The adapted Wasserstein distance controls the calibration errors of optimal values in various stochastic optimization problems, pricing and hedging problems, optimal stopping problems, etc. However, statistical aspects of the adapted…
Causal optimal transport and adapted Wasserstein distance have applications in different fields from optimization to mathematical finance and machine learning. The goal of this article is to provide equivalent formulations of these concepts…
We analyze the effect of small changes in the underlying probabilistic model on the value of multi-period stochastic optimization problems and optimal stopping problems. We work in finite discrete time and measure these changes with the…
The topology of weak convergence does not account for the growth of information over time that is captured in the filtration of an adapted stochastic process. For example, two adapted stochastic processes can have very similar laws but give…
Assume that an agent models a financial asset through a measure Q with the goal to price / hedge some derivative or optimize some expected utility. Even if the model Q is chosen in the most skilful and sophisticated way, she is left with…
The paper studies the robustness properties of discrete-time stochastic optimal control under Wasserstein model approximation for both discounted-cost and average-cost criteria. Specifically, we study the performance loss when applying an…
We investigate barycenters of Gaussian process laws in adapted Wasserstein space. The adapted Wasserstein distance refines classical optimal transport by enforcing compatibility of transport plans with the temporal flow of information, and…
Over the years a number of topologies for the set of laws of stochastic processes have been proposed. Building on the weak topology they all aim to capture more accurately the temporal structure of the processes. In a parallel paper we show…
The question of optimally approximating an arbitrary probability measure in the Wasserstein distance by a discrete one with uniform weights is considered. Estimates are obtained for the optimal approximation distance, with an explicit rate…
Wasserstein distance induces a natural Riemannian structure for the probabilities on the Euclidean space. This insight of classical transport theory is fundamental for tremendous applications in various fields of pure and applied…
Motivated by the statistical and computational challenges of computing Wasserstein distances in high-dimensional contexts, machine learning researchers have defined modified Wasserstein distances based on computing distances between…
In this paper, we establish sharp upper and lower bounds on the convergence rate of the empirical measures of point processes under the Wasserstein distance. To this end, we first introduce a new metric on the space of counting measures…
This brief note aims to introduce the recent paradigm of distributional robustness in the field of shape and topology optimization. Acknowledging that the probability law of uncertain physical data is rarely known beyond a rough…
This paper derives non-asymptotic error bounds for nonlinear stochastic approximation algorithms in the Wasserstein-$p$ distance. To obtain explicit finite-sample guarantees for the last iterate, we develop a coupling argument that compares…