General transmission theory of transient coherence of optical fields in dispersive fibers is shown. Temporal and spatial coherence properties of optical waves in random gradient fibers excited by partially coherent sources are studied by stochastic process theory for irregularities along fibers. Generalized coupling equations concerned with transient mutual correlation functions of random fields are derived. Using transient mutual correlation functions, exact spectral transfer functions for base band power responses are discussed with dispersive effects. Based on this theory, optical pulse signals in gradient fibers with radially inhomogeneous refractive index and lossy cladding that gives excellent filtering properties are studied. Scattering, pulse broadening, and base band power response are discussed.