5 papers
A numerical approach to Kolmogorov equation in high dimension based on Gaussian analysis
Franco Flandoli, Dejun Luo, Cristiano Ricci
For Kolmogorov equations associated to finite dimensional stochastic differential equations (SDEs) in high dimension, a numerical method alternative to Monte Carlo simulations is p…
Point vortex approximation for 2D Navier--Stokes equations driven by space-time white noise
Franco Flandoli, Dejun Luo
We show that the system of point vortices, perturbed by a certain transport type noise, converges weakly to the vorticity form of 2D Navier--Stokes equations driven by the space-ti…
Energy conditional measures and 2D turbulence
Franco Flandoli, Dejun Luo
We show that the invariant measure of point vortices, when conditioning the Hamiltonian to a finite interval, converges weakly to the enstrophy measure by conditioning the renormal…
The log-Sobolev inequality for the ground state of a Schrödinger operator on bounded convex domains
Huaiqian Li, Dejun Luo
We consider the ground state of the Schrödinger operator on the bounded convex domain , satisfying the Dirichlet boundary condition. Assume that $V\in…
The Weitzenbock formula on the Wiener space and its application to the asymptotic estimate of entropy
Dejun Luo
We consider the Fokker-Planck equation on the abstract Wiener space associated to the Ornstein-Uhlenbeck operator. Using the Weitzenböck formula, we prove an explicit estimate on t…