309 citations · 812 across the 46 of their papers we have counts for
49 papers
Fluctuations of stochastic PDEs with long-range correlations
Luca Gerolla, Martin Hairer, Xue-Mei Li
We study the large-scale dynamics of the solution to a nonlinear stochastic heat equation (SHE) in dimensions with long-range dependence. This equation is driven by mult…
Coarse Ricci curvature of weighted Riemannian manifolds
Marc Arnaudon, Xue-Mei Li, Benedikt Petko
We show that the generalized Ricci tensor of a weighted complete Riemannian manifold can be retrieved asymptotically from a scaled metric derivative of Wasserstein 1-distances betw…
On the (Non-)Stationary Density of Fractional-Driven Stochastic Differential Equations
Xue-Mei Li, Fabien Panloup, Julian Sieber
We investigate the stationary measure of SDEs driven by additive fractional noise with any Hurst parameter and establish that admits a smooth Lebesgue density obeying both…
An averaging principle for a completely integrable stochastic Hamiltonian system
Xue-Mei Li
We investigate the effective behaviour of a small transversal perturbation of order to a completely integrable stochastic Hamiltonian system, by which we mean a stochastic diff…
Generating diffusions with fractional Brownian motion
Martin Hairer, Xue-Mei Li
We study fast / slow systems driven by a fractional Brownian motion with Hurst parameter . Surprisingly, the slow dynamic converges on suitable timescales t…
Mild Stochastic Sewing Lemma, SPDE in Random Environment, and Fractional Averaging
Xue-Mei Li, Julian Sieber
Our first result is a stochastic sewing lemma with quantitative estimates for mild incremental processes, with which we study SPDEs driven by fractional Brownian motions in a rando…