Related papers: Stochastic sewing lemma on Wasserstein space

We introduce the first probabilistic framework tailored for sequential random projection, an approach rooted in the challenges of sequential decision-making under uncertainty. The analysis is complicated by the sequential dependence and…

A number of researchers have independently introduced topologies on the set of laws of stochastic processes that extend the usual weak topology. Depending on the respective scientific background this was motivated by applications and…

Stochastic processes offer a flexible mathematical formalism to model and reason about systems. Most analysis tools, however, start from the premises that models are fully specified, so that any parameters controlling the system's dynamics…

We introduce a framework for generating samples of a distribution given a finite number of its moments, targeted to particle-based solutions of kinetic equations and rarefied gas flow simulations. Our model, referred to as the…

We introduce a class of backward stochastic differential equations (BSDEs) on the Wasserstein space of probability measures. This formulation extends the classical correspondence between BSDEs, stochastic control, and partial differential…

In this paper, we study the stochastic Hamiltonian flow in Wasserstein manifold, the probability density space equipped with $L^2$-Wasserstein metric tensor, via the Wong--Zakai approximation. We begin our investigation by showing that the…

We study the convergence of stochastic time-discretization schemes for evolution equations driven by random velocity fields, including examples like stochastic gradient descent and interacting particle systems. Using a unified framework…

Random measures provide flexible parameters for Bayesian nonparametric models. Given two different priors for a random measure, we develop a natural framework to investigate the rate at which the corresponding posteriors merge, as the…

We study the problem of estimating a sequence of evolving probability distributions from historical data, where the underlying distribution changes over time in a nonstationary and nonparametric manner. To capture gradual changes, we…

This paper studies iterative schemes for measure transfer and approximation problems, which are defined through a slicing-and-matching procedure. Similar to the sliced Wasserstein distance, these schemes benefit from the availability of…

Using the Wiener-Hopf factorization, it is shown that it is possible to bound the path of an arbitrary Levy process above and below by the paths of two random walks. These walks have the same step distribution, but different random starting…

Random probabilities are a key component to many nonparametric methods in Statistics and Machine Learning. To quantify comparisons between different laws of random probabilities several works are starting to use the elegant Wasserstein over…

In this article, we merge celebrated results of Kesten and Spitzer [Z. Wahrsch. Verw. Gebiete 50 (1979) 5-25] and Kawazu and Kesten [J. Stat. Phys. 37 (1984) 561-575]. A random walk performs a motion in an i.i.d. environment and observes an…

We introduce LOT Wassmap, a computationally feasible algorithm to uncover low-dimensional structures in the Wasserstein space. The algorithm is motivated by the observation that many datasets are naturally interpreted as probability…

We derive moment estimates and a strong limit theorem for space inverses of stochastic flows generated by jump SDEs with adapted coefficients in weighted H\"older norms using the Sobolev embedding theorem and the change of variable formula.…

The Wasserstein distance is a distance between two probability distributions and has recently gained increasing popularity in statistics and machine learning, owing to its attractive properties. One important approach to extending this…

This manuscript presents an innovative framework for constructing barrier functions to bound reachability probabilities for continuous-time stochastic systems described by stochastic differential equations (SDEs). The reachability…

We develop a new method for showing that a given sequence of random variables verifies an appropriate law of the iterated logarithm. Our tools involve the use of general estimates on multidimensional Wasserstein distances, that are in turn…

We model stochastic choice as environment-dependent switching among a small library of deterministic decision rules. A Random Rule Model generates menu-level choice probabilities via named, interpretable rules weighted by observable menu…

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…