We exploit the separation of the filtering and control aspects of quantum feedback control to consider the optimal control as a classical stochastic problem on the space of quantum states. We derive the corresponding Hamilton-Jacobi-Bellman equations using the elementary arguments of classical control theory and show that this is equivalent, in the Stratonovich calculus, to a stochastic Hamilto...

We introduce a Mellin transform of functions which live on all of R and discuss its applications to the limiting theory of Bellman-Harris processes, and specifically Luria-Delbrück processes. More precisely, we calculate the life-time distribution of particles in a Bellman-Harris process from their first-generation offspring and limiting distributions, and prove a formula for the Laplace transf...

Actor-Critic Method for High Dimensional Static Hamilton--Jacobi--Bellman Partial Differential Equations based on Neural Networks

A solution of a discrete Hamilton–Jacobi–Bellman equation is represented in terms of idempotent analysis as a convergent series of integral operators.