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.
Numerical Analysis and Computation | Probability
J.-L. Menaldi and M. Robin. Singular ergodic control for multidimensional Gaussian-Poisson processes. Stochastics, 85:682-691, 2013 . doi: 10.1080/17442508.2013.795569