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Closed from expressing are derived for various statistical functions that arise in optical propagation through arbitrary optical systems that can be characterized by a complex ABCD matrix in distributed random inhomogeneities along the optical path. Specifically, within the second-order Rytov approximation, explicit general expressions are presented for the mutual coherence function, the log-amplitude and phase correlation function, and the mean square irradiance that is obtained in propagation through an arbitrary paraxial ABCD optical system containing Gaussian-shaped limiting apertures. Additionally, we consider the performance of adaptive-optics systems through arbitrary real paraxial ABCD optical systems and derive an expression for the mean irradiance of an adaptive-optics laser transmitter through such systems. Keywords: Gaussian beams; Optical propagation; Statistical optics; Turbulence.