We characterize the optimal control for a class of singular stochastic control problems as the unique solution to a related Skorokhod reflection problem. The considered optimization problems concern the minimization of a discounted cost functional over an infinite time-horizon through a process...

We provide an abstract framework for submodular mean field games and identify verifiable sufficient conditions that allow to prove existence and approximation of strong mean field equilibria in models where data may not be continuous with respect to the measure parameter and common noise is...

We provide an abstract framework for submodular mean field games and identify verifiable sufficient conditions that allow to prove existence and approximation of strong mean field equilibria in models where data may not be continuous with respect to the measure parameter and common noise is...

We consider an optimal control problem for a one-dimensional Itô diffusion and a stochastic game of optimal stopping associated with it. Their value functions satisfy ... and an optimal control defines a saddle point for the game. This extends earlier results to the case of bounded variation...

We study the stability of subcritical multi-class queueing networks with feedback allowed and a work-conserving head-of-the-line service discipline. Assuming that the fluid limit model associated to the queueing network satisfies a state space collapse condition, we show that the queueing...

We study the stability of subcritical multi-class queueing networks with feedback allowed and a work-conserving head-of-the-line service discipline. Assuming that the fluid limit model associated to the queueing network satisfies a state space collapse condition, we show that the queueing...

For stochastic differential equations reflecting on the boundary of a connected interval in R we discuss the problem of approximation for solutions. The main results are convergence in law as well as in Lp of discrete schemes that fundamentally generalize the classical Euler and Euler–Peano...

Constrained diffusions, with diffusion matrix scaled by small ϵ0, in a convex polyhedral cone G⊂Rk, are considered. Under suitable stability assumptions small noise asymptotic properties of invariant measures and exit times from domains are studied. Let B⊂G be a bounded domain. Under...