Process discovery studies algorithms for constructing process models that describe control flow of systems that generated given event logs, where an event log is a recording of executed traces of a system, with each trace captured as a sequence of executed actions. Traditional process discovery relies on an event log recorded and stored in a centralized repository. However, in distributed environments, such as cross-organizational process discovery, this centralization raises concerns about data availability, privacy, and high communication and bandwidth demands. To address these challenges, this paper introduces a novel Federated Stochastic Process Discovery (FSPD) approach. FSPD avoids centralized event logs by retaining them in decentralized silos, at organizations where they were originally recorded. Process discovery is then performed locally within each organization on its event log, and the resulting local models are shared with a central server for aggregation into a global model. Our evaluations on industrial event logs demonstrate that FSPD effectively constructs global process models while preserving organizational autonomy and privacy, providing a scalable and robust solution for process discovery in distributed settings.