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MPIPKS:
Stochastic processes
Abstract:
Among Markovian processes, the hallmark of Levy flights is
superdiffusion, or faster-than-Brownian dynamics. Here we show that Levy
laws, as well as Gaussian distributions, can also be the limit
distributions of processes with long-range memory that exhibit very slow
diffusion, logarithmic in time. These processes are path dependent and
anomalous motion emerges from frequent relocations to already visited
sites. We show how the central limit theorem is modified in this
context, keeping the usual distinction between analytic and nonanalytic
characteristic functions. A fluctuation-dissipation relation is also
derived. Our results may have important applications in the study of
animal and human displacements.
