Abstract Mean-Field Game (MFG) serves as a crucial mathematical framework in modeling
the collective behavior of individual agents interacting stochastically with a large population …

The turnpike property in contemporary macroeconomics asserts that if an economic planner
seeks to move an economy from one level of capital to another, then the most efficient path …

Motivated by entropic optimal transport, time reversal of diffusion processes is revisited. An
integration by parts formula is derived for the carré du champ of a Markov process in an …

We investigate the convergence rate of the optimal entropic cost v ε to the optimal transport
cost as the noise parameter ε↓ 0. We show that for a large class of cost functions c on R d× …

In the recent years the Schrödinger problem has gained a lot of attention because of the
connection, in the small-noise regime, with the Monge-Kantorovich optimal transport …

In this article, we study the mean field limit of weakly interacting diffusions for confining and
interaction potentials that are not necessarily convex. We explore the relationship between …

A pathwise large deviation principle in the Wasserstein topology and a pathwise central limit
theorem are proved for the empirical measure of a mean-field system of interacting …

We study a class of variational problems for regularized conservation laws with Lax's
entropy-entropy flux pairs. We first introduce a modified optimal transport space based on …

We show non-asymptotic exponential convergence of Sinkhorn iterates to the Schr\" odinger
potentials, solutions of the quadratic Entropic Optimal Transport problem on $\mathbb {R}^ d …

We investigate the long time behavior of weakly dissipative semilinear Hamilton–Jacobi–
Bellman (HJB) equations and the turnpike property for the corresponding stochastic control …