Non-stationary Markovian Replication Process causing Diverse Diffusions

Abstract

We introduce a single generative mechanism with which it is able to describe diverse non-stationary diffusions. A non-stationary Markovian replication process for steps is considered, for which we analytically derive time-evolution of the probability distribution of the walker's displacement and the generalized telegrapher equation with time-varying coefficients, and find that diffusivity can be determined by temporal changes of replication of a immediate step. By controlling the replications, we realize the diverse diffusions such as alternating diffusions, superdiffusions, subdiffusions, and marginal diffusions which are originated from oscillating, increasing,decreasing, and slowly increasing or decreasing replications with time, respectively.