A stochastic control method includes measuring a fluid property of a drilling fluid circulating within a mud circulation system and identifying a mud circulation model that dictates operation of the mud circulation system. The mud circulation model is based on one or more models of one or more uncertainties encountered during a wellbore drilling operation. The method further includes determining an accuracy of the mud circulation model based on a residue between the measured fluid property of the drilling fluid and a fluid property of the drilling fluid as provided by the mud circulation model, and programming a controller of the mud circulation system based on the mud circulation model to modify operation of the mud circulation system.