Viscosity solutions methods are used to pass to the limit in some penalization problems for rst order and second order, degenerate parabolic, Hamilton-Jacobi-Bellman equations. This characterizes theâ€¦ (More)

We develop a direct Lyapunov method for the almost sure open-loop stabilizability and asymptotic stabilizability of controlled degenerate diffusion processes. The infinitesimal decrease condition forâ€¦ (More)

We consider N -person differential games involving linear systems affected by white noise, running cost quadratic in the control and in the displacement of the state from a reference position, andâ€¦ (More)

Given a family of vector fields we introduce a notion of convexity and of semiconvexity of a function along the trajectories of the fields and give infinitesimal characterizations in terms ofâ€¦ (More)

We construct a generalized viscosity solution of the Dirich let problem for fully nonlinear degenerate elliptic equations in general domain s by the Perron-WienerBrelot method. The result is designedâ€¦ (More)

We study general 2nd order fully nonlinear degenerate elliptic equations on an arbitrary closed set with generalized Dirichlet boundary conditions in the viscosity sense. We prove some properties ofâ€¦ (More)

We study singular perturbations of a class of stochastic control problems under assumptions motivated by models of financial markets with stochastic volatilities evolving on a fast time scale. Weâ€¦ (More)

We describe the set of propagation of maxima of upper semicontinuous viscosity subsolutions of fully nonlinear, degenerate elliptic Hamilton-Jacobi-Bellman equations in the concave case, i.e., forâ€¦ (More)

We study singular perturbations of optimal stochastic control problems and differential games arising in the dimension reduction of system with multiple time scales. We analyze the uniformâ€¦ (More)

We present and study a notion of ergodicity for deterministic zerosum differential games that extends the one in classical ergodic control theory to systems with two conflicting controllers. We showâ€¦ (More)