On ergodic stopping and impulsive control problems for nonuniformly ergodic Markov processes

In this paper we study optimal stopping and impulse control with a long-run average cost functional for ergodic Markov processes, which transition semigroupP _t converges uniformly on compact sets to a unique invariant measure, ast. We restrict the class of strategies to so-called stopping rules and obtain continuity of value functions and characterization of optimal rules.     

Phonon modes at the 2H-NbSe2 surface observed by grazing incidence inelastic x-ray scattering

We have determined the dispersion of acoustic and optical surface phonon modes 2H-NbSe2 at the by inelastic x-ray scattering under grazing incidence conditions. Already, at room temperature, an anomaly is observed close to the charge density wave -vector position located at about one-third along the Gamma-M direction of the Brillouin zone. Our results indicate that the anomaly for the surface mode occurs at a lower energy than that measured in bulk sensitive geometry in the same experiment, showing evidence of a modified behavior in the uppermost layers. We demonstrate that inelastic x-ray scattering in grazing incidence conditions provides a unique tool to selectively study either surface or bulk lattice dynamics in a single experiment.     

Infinite horizon stopping problems with (nearly) total reward criteria

We study an infinite horizon optimal stopping Markov problem which is either undiscounted (total reward) or with a general Markovian discount rate. Using ergodic properties of the underlying Markov process, we establish the feasibility of the stopping problem and prove the existence of optimal and ε$\epsilon$-optimal stopping times. We show the continuity of the value function and its variational characterisation (in the viscosity sense) under different sets of assumptions satisfied by large classes of diffusion and jump–diffusion processes. In the case of a general discounted problem we relax a classical assumption that the discount rate is uniformly separated from zero.