We introduce COT-GAN, an adversarial algorithm to train implicit generative models
optimized for producing sequential data. The loss function of this algorithm is formulated …

At the end of the 1970s, Jean Jacod, Thierry Jeulin and Marc Yor started a systematic study
of enlargement of filtration which focuses on the properties of stochastic processes under a …

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 (Ann. Appl. Probab …

Assume that an agent models a financial asset through a measure ℚ with the goal to
price/hedge some derivative or optimise some expected utility. Even if the model ℚ is …

VI Bogachev, “Kantorovich problem of optimal transportation of measures: new directions of
research”, Uspekhi Mat. Nauk, 77:5(467) (2022), 3–52; Russian Math. Surveys, 77:5 (2022) …

We study representations of data from an arbitrary metric space χ in the space of univariate
Gaussian mixtures equipped with a transport metric (Delon and Desolneux 2020). We prove …

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 …

Wasserstein distance induces a natural Riemannian structure for the probabilities on the
Euclidean space. This insight of classical transport theory is fundamental for tremendous …

Mathematical models, calibrated to data, have become ubiquitous to make key decision
processes in modern quantitative finance. In this work, we propose a novel framework for …

Treatment effect estimation helps answer questions, such as whether a specific treatment
affects the outcome of interest. One fundamental issue in this research is to alleviate the …