Stochastic diffusion : from Markov to non-Markov modeling

We briefly discuss omnipresence of stochastic modeling in physical science by recalling definitions of Markovian diffusion and generally, non-Markovian continuous time random walks (CTRW). If the motion of an idealized system can be described by a sum of independent displacements whose statistic over short time intervals has a well defined variance, the resulting random walk converges to a normal diffusion process. In turn, if formulation of such motion assumes the idea of distribution of waiting times between subsequent steps, the CTRW scenario emerges, which typically violates the Markovian property.