Abstract
The purpose of this paper is to introduce the concept of closed-loop control of a stochastic process associated with the motion of a nonrelativistic random particle without spin in a given deterministic field of the Euclidean space. The state equation is a Fokker-Planck equation in which the drift is the value of the control depending on the past or future values of the state. It is shown that such an equation can be derived without Markovian assumption. For a particular choice of the control, the state equation reduces to a continuity equation along the lines of the given field. The stochastic processes having the state as first probability density have also their conditional probability density depending on the state in such a way that they are not Markovian in general.
Published Version
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