The two-state model for anomalous stochastic motion

The two-state model (TSM) with the anomalous long-tailed transition kinetics is analyzed. The TSM relaxation kinetics is found to have some peculiarities. The diffusion TSM, in which a probe particle is assumed to diffuse in both states but with different diffusion coefficients, is also considered. The diffusion TSM predicts some specific features of anomalous diffusion and diffusion-assisted activated rate processes.