Volume 96, Number 6, December 2011
|Number of page(s)||6|
|Published online||07 December 2011|
Herding model and 1/f noise
Institute of Theoretical Physics and Astronomy, Vilnius University - A. Goštauto 12, LT-01108 Vilnius, Lithuania, EU
Accepted: 1 November 2011
We provide evidence that for some values of the parameters a simple agent-based model, describing herding behavior, yields signals with 1/f power spectral density. We derive a non-linear stochastic differential equation for the ratio of number of agents and show, that it has the form proposed earlier for modeling of 1/fβ noise with different exponents β. The non-linear terms in the transition probabilities, quantifying the herding behavior, are crucial to the appearance of 1/f noise. Thus, the herding dynamics can be seen as a microscopic explanation of the proposed non-linear stochastic differential equations generating signals with 1/fβ spectrum. We also consider the possible feedback of macroscopic state on microscopic transition probabilities strengthening the non-linearity of equations and providing more opportunities in the modeling of processes exhibiting power-law statistics.
PACS: 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 89.65.Gh – Economics; econophysics, financial markets, business and management / 05.10.Gg – Stochastic analysis methods (Fokker-Planck, Langevin, etc.)
© EPLA, 2011
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.