Characterization and memory effects in stochastic processes

Abstract

The main purpose of this project is the study of anomalous diffusion in complex non Markovian discrete-time Random Walk systems with strong long range time-memory correlations. Specifically, we focus on systems with full memory and systems with memory damage, the latter being those in which the recent memory has been erased. The question of mapping non-Markovian processes in Markovian processes is discussed. A relation between log-periodic corrections to scaling and anomalous diffusion is analysed through the introduction of pauses in the RW, both in 1D and 2D. Lévy processes are also taken into account by searching for a connection among suitably chosen time-discrete RW memory patterns and Lévy originated processes. The scaling behavior of the Self Avoiding Walk is also addressed using a recently developed method of analysis for studying universality, criticality and conformational properties of systems, with possible applications to polymers, biopolymers and magnetic systems. (AU)