Functional equation for the crossover in a model of one-dimensional Weierstrass random walks

Summary (translated from the Russian): "Within the framework of the Weierstrass-type Markov random walks approach, we examine the problem of one-dimensional symmetric diffusion using two-parameter scaling for the transition probability. We construct the solution to a functional equation for the Lyapunov characteristic function in the form of a sum of regular (homogeneous) and singular (nonhomogeneous) solutions, and we find conditions for the crossover from normal to anomalous diffusion."