Optimal Control for a Linear Quadratic Problem with a Stochastic Time Scale
We consider a linear-quadratic control problem where a time parameter evolves according to a stochastic time scale. The stochastic time scale is defined via a stochastic process with continuously differentiable paths. We obtain an optimal infinite-time control law under criteria similar to the long-run averages. Some examples of stochastic time scales from various applications have been examined.