Energy-Efficient Pursuit of Multidimensional Wiener Processes

We consider the problem of construction of energy-efficient Markov approximations (pursuit strategies) of a multidimensional Wiener process. In a certain natural class of pursuit strategies, we find an optimal strategy and obtain the asymptotics of the minimal pursuit energy on large time intervals. We also establish a correspondence between a Wiener process contained in the unit ball and an energy-efficient approximation. A relation to the minimization problem of Fisher information is revealed.