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We investigate the decentralized diagnosis of stochastic discrete event systems (SDESs) by using multiple local stochastic diagnosers, each possessing its own sensors to deal with different information. We formalize the notions of decentralized diagnosis for SDESs by defining the concept of codiagnosability for stochastic automata, in which any communication among the local stochastic diagnosers or to any coordinators is not involved. These notions are weaker than the corresponding notions of decentralized diagnosis of classical DESs. A stochastic system being codiagnosable means that a fault can be detected by at least one local stochastic diagnoser within a finite delay. We construct a codiagnoser from a given stochastic system with a finite number of projections whose each diagnosis component uses the complete model of the system. We also deal with a number of basic properties of the codiagnoser. In particular, a necessary and sufficient condition of the codiagnosability for SDESs is presented, which generalizes the corresponding results of centralized diagnosis for SDESs. Also, we give a computing method in detail to check the codiagnosability of SDESs. As an application of our results, some examples are described.