This work develops first a general model for Coherent Digital Transmission Systems in presence of thermal noise and intersymbol interference arriving at error probabilities expressions for several modulation systems. Methods of approximate calculations of error probabilities based on moments of received interference samples are presented and analyzed. Comparisons are made between methods for calculating moments of sums of random variables. Comparisons between methods for approximating error probabilities are also made. It was found Gauss Quadrature Rule method for approximating these error probabilities was more efficient then Gram-Charlier Series method. It was also found possible to reduce calculations into a unidimensional problem, even in bidimensional modulation systems. At the end several applications of methods are shown.