6 papers · 1 filter
Dimension reduction techniques in deterministic mean field games
Jean-Michel Lasry, Pierre-Louis Lions, Benjamin Seeger
We present examples of equations arising in the theory of mean field games that can be reduced to a system in smaller dimensions. Such examples come up in certain applications, and…
Hölder regularity of Hamilton-Jacobi equations with stochastic forcing
Pierre Cardaliaguet, Benjamin Seeger
We obtain space-time Hölder regularity estimates for solutions of first- and second-order Hamilton-Jacobi equations perturbed with an additive stochastic forcing term. The bounds d…
Interpolation results for pathwise Hamilton-Jacobi equations
Pierre-Louis Lions, Benjamin Seeger, Panagiotis Souganidis
We study the interplay between the regularity of paths and Hamiltonians in the theory of pathwise Hamilton-Jacobi equations with the use of interpolation methods. The regularity of…
Homogenization of a stochastically forced Hamilton-Jacobi equation
Benjamin Seeger
We study the homogenization of a Hamilton-Jacobi equation forced by rapidly oscillating noise that is colored in space and white in time. It is shown that the homogenized equation…
Scaling limits and homogenization of mixing Hamilton-Jacobi equations
Benjamin Seeger
We study the homogenization of nonlinear, first-order equations with highly oscillatory mixing spatio-temporal dependence. It is shown in a variety of settings that the homogenized…
Approximation schemes for viscosity solutions of fully nonlinear stochastic partial differential equations
Benjamin Seeger
The aim of this paper is to develop a general method for constructing approximation schemes for viscosity solutions of fully nonlinear pathwise stochastic partial differential equa…