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The presence of recurring arrhythmic events (also known as cardiac dysrhythmia or irregular heartbeats), as well as erroneous beat detection due to low signal quality, significantly affects estimation of both time and frequency domain indices of heart rate variability (HRV). A reliable, real-time classification and correction of ECG-derived heartbeats is a necessary prerequisite for an accurate online monitoring of HRV and cardiovascular control. We have developed a novel point-process-based method for real-time R-R interval error detection and correction. Given an R-wave event, we assume that the length of the next R-R interval follows a physiologically motivated, time-varying inverse Gaussian probability distribution. We then devise an instantaneous automated detection and correction procedure for erroneous and arrhythmic beats by using the information on the probability of occurrence of the observed beat provided by the model. We test our algorithm over two datasets from the PhysioNet archive. The Fantasia normal rhythm database is artificially corrupted with known erroneous beats to test both the detection procedure and correction procedure. The benchmark MIT-BIH Arrhythmia database is further considered to test the detection procedure of real arrhythmic events and compare it with results from previously published algorithms. Our automated algorithm represents an improvement over previous procedures, with best specificity for the detection of correct beats, as well as highest sensitivity to missed and extra beats, artificially misplaced beats, and for real arrhythmic events. A near-optimal heartbeat classification and correction, together with the ability to adapt to time-varying changes of heartbeat dynamics in an online fashion, may provide a solid base for building a more reliable real-time HRV monitoring device.