8 citations · 10 across the 10 of their papers we have counts for
16 papers
A comparison principle for semilinear Hamilton-Jacobi-Bellman equations in the Wasserstein space
Samuel Daudin, Benjamin Seeger
The goal of this paper is to prove a comparison principle for viscosity solutions of semilinear Hamilton-Jacobi equations in the space of probability measures. The method involves…
Linear and nonlinear transport equations with coordinate-wise increasing velocity fields
Pierre-Louis Lions, Benjamin Seeger
We consider linear and nonlinear transport equations with irregular velocity fields, motivated by models coming from mean field games. The velocity fields are assumed to increase i…
Transport equations and flows with one-sided Lipschitz velocity fields
Pierre-Louis Lions, Benjamin Seeger
We study first- and second-order linear transport equations, as well as ODE and SDE flows, with velocity fields satisfying a one-sided Lipschitz condition. Depending on the time di…
Mean field games with common noise and degenerate idiosyncratic noise
Pierre Cardaliaguet, Benjamin Seeger, Panagiotis Souganidis
We study the forward-backward system of stochastic partial differential equations describing a mean field game for a large population of small players subject to both idiosyncratic…
The Neumann problem for fully nonlinear SPDE
Paul Gassiat, Benjamin Seeger
We generalize the notion of pathwise viscosity solutions, put forward by Lions and Souganidis to study fully nonlinear stochastic partial differential equations, to equations set o…
Besov rough path analysis
Peter Friz, Benjamin Seeger
Rough path analysis is developed in the full Besov scale. This extends, and essentially concludes, an investigation started by [Prömel--Trabs, Rough differential equations driven b…
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…
Perron's method for pathwise viscosity solutions
Benjamin Seeger
We use Perron's method to construct viscosity solutions of fully nonlinear degenerate parabolic pathwise (rough) partial differential equations. This provides an intrinsic method f…
Homogenization of pathwise Hamilton-Jacobi equations
Benjamin Seeger
We present qualitative and quantitative homogenization results for pathwise Hamilton-Jacobi equations with "rough" multiplicative driving signals. When there is only one such signa…
Homogenization of Hamilton-Jacobi equations with rough time dependence
Benjamin Seeger
We consider viscosity solutions of Hamilton-Jacobi equations with oscillatory spatial dependence and rough time dependence. The time dependence is in the form of the derivative of…
On the Size of the Resonant Set for the Products of 2x2 Matrices
Jeffrey Allen, Benjamin Seeger, Deborah Unger
For θ \in [0, 2π), consider the rotation matrix R? and h = (λ, 0; 0, 0), λ > 1. Let W_n(θ) denote the product of m R?'s and n h's with the condition m \leq [ε\astn], (0 < ε< 1). We…