This article concerns fault diagnosis and prognosis for stochastic discrete event systems. For this purpose, partially observed stochastic Petri nets are introduced that include the sensors used to measure events and markings and the Markovian stochastic dynamics used to represent failure processes. Timed observation sequences result from this modeling, and the probabilities of timed and untimed marking trajectories consistent with a given timed observation sequence are systematically computed. Diagnosis in terms of fault probability is obtained as a consequence and compared with the belief of faults that is usually used for diagnosis issues. Confidence factors based on fault probabilities are also proposed. Finally, state estimation and fault prediction are investigated, and probability of future faults is obtained as a consequence. An application case is studied to illustrate the method.