Related papers: Error estimates for finite difference schemes asso…
We obtain an error estimate between viscosity solutions and \delta-viscosity solutions of nonhomogeneous fully nonlinear uniformly elliptic equations. The main assumption, besides uniform ellipticity, is that the nonlinearity is…
We consider the computation of free energy-like quantities for diffusions in high dimension, when resorting to Monte Carlo simulation is necessary. Such stochastic computations typically suffer from high variance, in particular in a low…
In this paper we study the fully nonlinear stochastic Hamilton-Jacobi-Bellman (HJB) equation for the optimal stochastic control problem of stochastic differential equations with random coefficients. The notion of viscosity solution is…
A junction is a particular network given by the collection of $N\ge 1$ half lines $[0,+\infty)$ glued together at the origin. On such a junction, we consider evolutive Hamilton-Jacobi equations with $N$ coercive Hamiltonians. Furthermore,we…
A Hamilton-Jacobi equation with Caputo's time-fractional derivative of order less than one is considered. The notion of a viscosity solution is introduced to prove unique existence of a solution to the initial value problem under periodic…
We study policy iteration (PI) for deterministic infinite-horizon discounted optimal control problems, whose value function is characterized by a stationary Hamilton--Jacobi--Bellman (HJB) equation. At the PDE level, PI is fundamentally…
In this article, the notion of viscosity solution is introduced for the path-dependent Hamilton-Jacobi-Bellman (PHJB) equations associated with the optimal control problems for path-dependent stochastic differential equations. We identify…
We study a selection problem for degenerate viscous Hamilton--Jacobi equations with convex Hamiltonians, in which the approximation procedure combines a nonlinear discounted approximation with a small potential perturbation. A key question…
We consider a class of "filtered" schemes for first order time dependent Hamilton-Jacobi equations and prove a general convergence result for this class of schemes. A typical filtered scheme is obtained mixing a high-order scheme and a…
We consider semi-discrete first-order finite difference schemes for a nonlinear degenerate convection-diffusion equations in one space dimension, and prove an L1 error estimate. Precisely, we show that the L1 loc difference between the…
This paper is devoted to the study of fully nonlinear stochastic Hamilton-Jacobi (HJ) equations for the optimal stochastic control problem of ordinary differential equations with random coefficients. Under the standard Lipschitz continuity…
In this paper, we study a Hamilton-Jacobi-Bellman (HJB) equation set on the Wasserstein space $\mathcal{P}_2(\mathbb{R}^d)$, with a second order term arising from a purely common noise. We do not assume that the Hamiltonian is convex in the…
A classical problem in ergodic continuous time control consists of studying the limit behavior of the optimal value of a discounted cost functional with infinite horizon as the discount factor $\lambda$ tends to zero. In the literature,…
We study the well-posedness of an infinite-dimensional Hamilton-Jacobi equation posed on the set of non-negative measures and with a monotonic non-linearity. Our results will be used in a companion work to propose a conjecture and prove…
In a previous work (Akian, Fodjo, 2016), we introduced a lower complexity probabilistic max-plus numerical method for solving fully nonlinear Hamilton-Jacobi-Bellman equations associated to diffusion control problems involving a finite…
In this paper we set up a rigorous justification for the reinitialization algorithm. Using the theory of viscosity solutions, we propose a well-posed Hamilton-Jacobi equation with a parameter, which is derived from homogenization for a…
Here, we study quantitative homogenization of first-order convex Hamilton-Jacobi equations with $(u/\varepsilon)$-periodic Hamiltonians which typically appear in dislocation dynamics. Firstly, we establish the optimal convergence rate by…
We consider the specified stochastic homogenization of first order evolutive Hamilton-Jacobi equations on a very simple junction, i.e the real line with a junction at the origin. Far from the origin, we assume that the considered…
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 leveraging differentiability properties of the…
In this article, a class of optimal control problems of differential equations with delays are investigated for which the associated Hamilton-Jacobi-Bellman (HJB) equations are nonlinear partial differential equations with delays. This type…