TY  - JOUR
AU  - Coletti, Cristian F.
AU  - Gava, Renato
AU  - Schütz, Gunter M.
TI  - Central limit theorem and related results for the elephant random walk
JO  - Journal of mathematical physics
VL  - 58
IS  - 5
SN  - 1089-7658
CY  - College Park, Md.
PB  - American Inst. of Physics
M1  - FZJ-2018-00124
SP  - 053303
PY  - 2017
AB  - We study the so-called elephant random walk (ERW) which is a non-Markovian discrete-time random walk on ℤ with unbounded memory which exhibits a phase transition from a diffusive to superdiffusive behavior. We prove a law of large numbers and a central limit theorem. Remarkably the central limit theorem applies not only to the diffusive regime but also to the phase transition point which is superdiffusive. Inside the superdiffusive regime, the ERW converges to a non-degenerate random variable which is not normal. We also obtain explicit expressions for the correlations of increments of the ERW
LB  - PUB:(DE-HGF)16
UR  - <Go to ISI:>//WOS:000402608000030
DO  - DOI:10.1063/1.4983566
UR  - https://juser.fz-juelich.de/record/841823
ER  -