Avoiding the Origin: a Finite-fuel Stochastic Control Problem
نویسنده
چکیده
We consider a model for the control of a satellite—fuel is expended in a linear fashion to move a satellite following a diffusion—the aim is to keep the satellite above a critical level. Under suitable assumptions on the drift and diffusion co-efficients, it is shown that the probability of the satellite falling below the critical level is minimised by a policy which moves the satellite a certain distance above the critical level and then imposes a reflecting boundary at this higher level until the fuel is exhausted.
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