Singular ergodic control for multidimensional Gaussian 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.

Multidimensional Wick-itô Formula for Gaussian Processes

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...

The Rate of Entropy for Gaussian Processes

In this paper, we show that in order to obtain the Tsallis entropy rate for stochastic processes, we can use the limit of conditional entropy, as it was done for the case of Shannon and Renyi entropy rates. Using that we can obtain Tsallis entropy rate for stationary Gaussian processes. Finally, we derive the relation between Renyi, Shannon and Tsallis entropy rates for stationary Gaussian proc...