Abstract
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 being to keep the satellite above a critical level. Under suitable assumptions on the drift and diffusion coefficients, it is shown that the probability of the satellite falling below the critical level is minimized by a policy that 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.
Citation
Saul Jacka. "Avoiding the origin: A finite-fuel stochastic control problem." Ann. Appl. Probab. 12 (4) 1378 - 1389, November 2002. https://doi.org/10.1214/aoap/1037125867
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