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We present a unified probabilistic point process framework to estimate and monitor the instantaneous heartbeat dynamics as related to specific cardiovascular control mechanisms and hemodynamics. Assessment of the model's statistics is established through the Wiener-Volterra theory and a multivariate autoregressive (AR) structure. A variety of instantaneous cardiovascular metrics, such as heart rate (HR), heart rate variability (HRV), respiratory sinus arrhythmia (RSA), and baroreceptor-cardiac reflex (baroreflex), can be rigorously derived within a parametric framework and instantaneously updated with an adaptive algorithm. Nonlinearity metrics, as well as the bispectrum of heartbeat intervals, can also be derived. We have applied the proposed point process framework to a number of recordings under different experimental protocols. Results reveal interesting dynamic trends across different posture/pharmacological/age/ heart disease conditions, pointing at our mathematical approach as a promising monitoring tool for an accurate, noninvasive assessment of a large spectrum of cardiovascular diseases and disorders, including hypertension and congestive heart disease.