Related papers: On ergodic control problem for viscous Hamilton--J…

We prove homogenization for a class of viscous Hamilton-Jacobi equations in the stationary and ergodic setting in one space dimension. Our assumptions include most notably the following: the Hamiltonian is of the form $G(p) + \beta…

In this paper we study ergodic backward stochastic differential equations (EBSDEs) dropping the strong dissipativity assumption needed in the previous work. In other words we do not need to require the uniform exponential decay of the…

In this paper, we establish the convergence of solutions to the viscous Hamilton-Jacobi equation (with a Tonelli Hamiltonian): \[ \lambda u +H(x, du)=\varepsilon(\lambda)\Delta u,\quad \lambda>0 \] as $\lambda\rightarrow 0_+$, once the…

We consider the homogenization of monotone systems of viscous Hamilton-Jacobi equations with convex nonlinearities set in the stationary, ergodic setting. The primary focus of this paper is on collapsing systems which, as the microscopic…

In this paper we study an optimal control problem associated to a linear degenerate elliptic equation with mixed boundary conditions. The equations of this type can exhibit the Lavrentieff phenomenon and non-uniqueness of weak solutions. We…

Motivated by applications in natural resource management, risk management, and finance, this paper is focused on an ergodic two-sided singular control problem for a general one-dimensional diffusion process. The control is given by a…

For $N$-body problems with homogeneous potentials we define a special class of central configurations related with the reduction of homotheties in the study of homogeneous weak KAM solutions. For potentials in $1/r^\alpha$ with $\alpha\in…

Bellman equations of ergodic type related to risk-sensitive control are considered. We treat the case that the nonlinear term is positive quadratic form on first-order partial derivatives of solution, which includes linear exponential…

For a Hamilton-Jacobi equation defined on a network, we introduce its vanishing viscosity approximation. The elliptic equation is given on the edges and coupled with Kirchhoff-type conditions at the transition vertices. We prove that there…

In this brief paper, we consider the problem of minimizing the asymptotic exit rate of diffusion processes from an open connected bounded set pertaining to a multi-channel system with small random perturbations. Specifically, we establish a…

This paper proposes a new framework to model control systems in which a dynamic friction occurs. The model consists in a controlled differential inclusion with a discontinuous right hand side, which still preserves existence and uniqueness…

We establish the existence and uniqueness of viscosity solutions within a domain $\Omega\subseteq\mathbb R^n$ for a class of equations governed by elliptic and eikonal type equations in disjoint regions. Our primary motivation stems from…

We derive the long time asymptotic of solutions to an evolutive Hamilton-Jacobi-Bellman equation in a bounded smooth domain, in connection with ergodic problems recently studied in \cite{bcr}. Our main assumption is an appropriate…

We consider an optimal control on networks in the spirit of the works of Achdou et al. (2013) and Imbert et al. (2013). The main new feature is that there are entry (or exit) costs at the edges of the network leading to a possible…

An optimal ergodic control problem (EC problem, for short) is investigated for a linear stochastic differential equation with quadratic cost functional. Constant nonhomogeneous terms, not all zero, appear in the state equation, which lead…

We consider homogenization for weakly coupled systems of Hamilton--Jacobi equations with fast switching rates. The fast switching rate terms force the solutions converge to the same limit, which is a solution of the effective equation. We…

A two-person zero-sum differential game with unbounded controls is considered. Under proper coercivity conditions, the upper and lower value functions are characterized as the unique viscosity solutions to the corresponding upper and lower…

General theorems for existence and uniqueness of viscosity solutions for Hamilton-Jacobi-Bellman quasi-variational inequalities (HJBQVI) with integral term are established. Such nonlinear partial integro-differential equations (PIDE) arise…

The present paper represents a continuation of our previous one. There, a continuous dependence result for the solution of an elliptic variational-hemivariational inequality was obtained and then used to prove the existence of optimal pairs…

We present a proof of qualitative stochastic homogenization for a nonconvex Hamilton-Jacobi equation. The new idea is to introduce a family of "sub-equations" and to control solutions of the original equation by the maximal subsolutions of…