In non-interconnected areas, the efficient use of renewable energies requires optimal management of electricity consumption. The site studied is the "Cirque de Mafate" on Reunion Island. Our laboratory has developed a mixed integer linear programming model which minimizes the electricity consumption of a cluster of houses. This model is deterministic. Our study focuses on the stochastic part, it aims to model, optimize and simulate the stochastic operation of an autonomous microgrid by mutualizing production and storage resources. A study for the solar resource forecasting is performed, using nonparametric methods for the estimation of probability density functions. Indeed, the prediction of the intermittent resource and the combination of production sources are the keys to the good functioning of a microgrid in autonomous mode. One of the strategies found is to aim for auto-consumption for three days if the solar forecast is pessimistic, a part of the energy is then reserved at the battery level for the next two days. The results allow to evaluate the performance of the system in front of random constraints and to make decisions.