Sustainability when capital management has stochastic consequences

Sustainability is usually defined as a requirement of each generation to manage its stocks of man-made and natural capital such that the utility that it ensures itself can be shared by all future generations. Here we extend this definition to the case where capital management does not have deterministic consequences. A characterization is offered where the sustainability of one generation's behavior can be determined by comparing its utility with the utility of the succeeding generation, provided that the latter behaves in a sustainable manner. The properties of the definition are investigated and illustrated.