Singular ergodic control for multidimensional Gaussian–Poisson processes

Singular ergodic control for multidimensional Gaussian processes

Singular Ergodic Control for Multidimensional Gaussian-Poisson Processes

Singular control for multidimensional Gaussian-Poisson processes with a long-run (or ergodic) and a discounted criteria are discussed. The dynamic programming yields the corresponding Hamilton-JacobiBellman equations, which are discussed. Full details on the proofs and further extensions are left for coming works.

Singular Perturbations in Ergodic Control of Diffusions

Ergodic control of a non-degenerate diffusion with two timescales is studied in the limiting case as the time-scale separation increases to infinity. It is shown that the limit problem is another ergodic control problem for the slow time-scale component alone with its dynamics averaged over the (controlled) invariant probability measures for the fast component. These measures in turn can be tre...

Ergodic control of diffusion processes

Results concerning existence and characterization of optimal controls for ergodic control of nondegenerate diffusion processes are described. Extensions to the general ‘controlled martingale problem’ are indicated, which cover in particular degenerate diffusions and some infinite dimensional problems. In conclusion, some related problems and open issues are discussed. Mathematics Subject Classi...

An Abelian Limit Approach to a Singular Ergodic Control Problem

We consider an ergodic stochastic control problem for a class of one-dimensional Itô processes where the available control is an added bounded variation process. The corresponding infinite horizon discounted control problem is solved in [28]. Here, we show that, as the discount factor approaches zero, the optimal strategies derived in [28] “converge” to an optimal strategy for the ergodic contr...