Volume 100, Number 6, December 2012
|Number of page(s)||6|
|Published online||04 January 2013|
Robustness of the non-Markovian Alzheimer walk under stochastic perturbation
1 Departamento de Física e Química, FCFRP, Universidade de São Paulo - 14040-903 Ribeirão Preto, SP, Brazil
2 Instituto de Física, Universidade Federal de Alagoas - Maceió, AL, 57072-970, Brazil
3 Departamento de Física Teórica e Experimental, Universidade Federal do Rio Grande do Norte Natal, RN, 59078-900, Brazil
Received: 25 September 2012
Accepted: 26 November 2012
The elephant walk model originally proposed by Schütz and Trimper to investigate non-Markovian processes led to the investigation of a series of other random-walk models. Of these, the best known is the Alzheimer walk model, because it was the first model shown to have amnestically induced persistence —i.e. superdiffusion caused by loss of memory. Here we study the robustness of the Alzheimer walk by adding a memoryless stochastic perturbation. Surprisingly, the solution of the perturbed model can be formally reduced to the solutions of the unperturbed model. Specifically, we give an exact solution of the perturbed model by finding a surjective mapping to the unperturbed model.
PACS: 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 05.70.Ln – Nonequilibrium and irreversible thermodynamics / 02.50.-r – Probability theory, stochastic processes, and statistics
© EPLA, 2012
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.