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Full-Text Articles in Physical Sciences and Mathematics
Singular Ergodic Control For Multidimensional Gaussian-Poisson Processes, J. L. Menaldi, M. Robin
Singular Ergodic Control For Multidimensional Gaussian-Poisson Processes, J. L. Menaldi, M. Robin
Mathematics Faculty Research Publications
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-Jacobi-Bellman equations, which are discussed. Full details on the proofs and further extensions are left for coming works.
Remarks On Risk-Sensitive Control Problems, José Luis Menaldi, Maurice Robin
Remarks On Risk-Sensitive Control Problems, José Luis Menaldi, Maurice Robin
Mathematics Faculty Research Publications
The main purpose of this paper is to investigate the asymptotic behavior of the discounted risk-sensitive control problem for periodic diffusion processes when the discount factor α goes to zero. If uα(θ, x) denotes the optimal cost function, being the risk factor, then it is shown that limα→0αuα(θ, x) = ξ(θ) where ξ(θ) is the average on ]0, θ[ of the optimal cost of the (usual) in nite horizon risk-sensitive control problem.
Singular Ergodic Control For Multidimensional Gaussian Processes, J. L. Menaldi, M. Robin, M. I. Taksar
Singular Ergodic Control For Multidimensional Gaussian Processes, J. L. Menaldi, M. Robin, M. I. Taksar
Mathematics Faculty Research Publications
A multidimensional Wiener process is controlled by an additive process of bounded variation. A convex nonnegative function measures the cost associated with the position of the state process, and the cost of controlling is proportional to the displacement induced. We minimize a limiting time-average expected (ergodic) criterion. Under reasonable assumptions, we prove that the optimal discounted cost converges to the optimal ergodic cost. Moreover, under some additional conditions there exists a convex Lipschitz continuous function solution to the corresponding Hamilton-Jacobi-Bellman equation which provides an optimal stationary feedback control.