Radio waveguides and diffusion processes on differentiable manifolds

One-mode waveguide with random inhomogeneities is considered. For both the case when losses are ignored and the case of non-zero losses, a diffusion approximation for the discrete Markov process of the reflection coefficient is obtained. Explicit formulas for the coefficients of the diffusion operator are derived. The results are compared with those of M. E. Gercenstein and V. B. Vasil'ev, V. N. Tutubalin, R. Burridge and G. Papanicolaou. It is shown that the Brownian motion process never appears in the models under consideration.