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Process mining is an emerging research area that applies the well-established data mining solutions to the challenging business process modeling problems. Mining streams of business processes in the real time as they are generated is a necessity to obtain an instant knowledge from big process data. In this paper, we introduce an efficient approach for exploring and counting process fragments from a stream of events to infer a process model using the Heuristics Miner algorithm. Our novel approach, called Str ProM, builds prefix-trees to extract sequential patterns of events from the stream. Str ProM uses a batch-based approach to continuously update and prune these prefix-trees. The final models are generated from those trees after applying a novel decaying mechanism over their statistics. The extensive experimental evaluation demonstrates the superiority of our approach over a state-of-the-art technique in …