Publicación: REINFORCED RANDOM WALKS UNDER MEMORY LAPSES
Fecha
2021
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JOURNAL OF STATISTICAL PHYSICS
Resumen
WE INTRODUCE A ONE-DIMENSIONAL RANDOM WALK, WHICH AT EACH STEP PERFORMS A REINFORCED DYNAMICS WITH PROBABILITY ? AND WITH PROBABILITY 1??, THE RANDOM WALK PERFORMS A STEP INDEPENDENT OF THE PAST. WE ANALYSE ITS ASYMPTOTIC BEHAVIOUR, SHOWING A LAW OF LARGE NUMBERS AND CHARACTERIZING THE DIFFUSIVE AND SUPERDIFFUSIVE REGIONS. WE PROVE CENTRAL LIMIT THEOREMS AND LAW OF ITERATED LOGARITHM BASED ON THE MARTINGALE APPROACH.
