Dynamical models of weak scattering

We extend a recent diffusion model, in which the continuous time dynamics of theK-scattering process have been proposed, to include the effect of the presence of acoherent offset in the scattering amplitude. The weak scattering amplitudes arecharacterized in terms of continuous time biased random walk models, and thecorresponding stochastic dynamics derived. The stochastic differential geometry ofthe resultant amplitude fluctuations is derived in relation to that of pureK-scattering. Asymptotic distributions of amplitude, intensity, and phase are provided,and the condition for detailed balance shown to hold.