Global (or network-aware) computing entails large-scale networks of computers performing tasks in a cooperative and coordinated manner. Programming and modeling languages such as Klaim focus on key functional aspects of global computing such as distribution awareness, (code and agent) mobility, and privacy aspects. This paper instead concentrates on their performance and dependability aspects. It proposes StoKlaim, an extension of Klaim which permits the description of random phenomena such as spontaneous computer crashes and spurious network hick ups. The operational semantics of StoKlaim is based on continuous- time Markov chains. The approach is illustrated by modeling the spreading of a virus through a network.