ИСТИНА

Initially developed in the framework of quantum stochastic calculus, the main equations of quantum stochastic filtering were later on derived as the limits of Markov models of discrete measurements under appropriate scaling. In many branches of modern physics it became popular to extend random walk modeling to the continuous time random walk (CTRW) modeling, where the time between discrete events is taken to be non-exponential. Here we apply the CTRW modeling to the continuous quantum measurements yielding the new fractional in time evolution equations of quantum filtering and thus new fractional equations of quantum mechanics of open systems. The related quantum control problems and games turn out to be described by the fractional Hamilton-Jacobi-Bellman (HJB) equations on Riemannian manifolds.