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Entropy 2017, 19(8), 387; https://doi.org/10.3390/e19080387

Spurious Memory in Non-Equilibrium Stochastic Models of Imitative Behavior

Institute of Theoretical Physics and Astronomy, Vilnius University, Saulėtekio al. 3, 10257 Vilnius, Lithuania
These authors contributed equally to this work.
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Received: 26 June 2017 / Revised: 21 July 2017 / Accepted: 24 July 2017 / Published: 27 July 2017
(This article belongs to the Special Issue Statistical Mechanics of Complex and Disordered Systems)
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Abstract

The origin of the long-range memory in non-equilibrium systems is still an open problem as the phenomenon can be reproduced using models based on Markov processes. In these cases, the notion of spurious memory is introduced. A good example of Markov processes with spurious memory is a stochastic process driven by a non-linear stochastic differential equation (SDE). This example is at odds with models built using fractional Brownian motion (fBm). We analyze the differences between these two cases seeking to establish possible empirical tests of the origin of the observed long-range memory. We investigate probability density functions (PDFs) of burst and inter-burst duration in numerically-obtained time series and compare with the results of fBm. Our analysis confirms that the characteristic feature of the processes described by a one-dimensional SDE is the power-law exponent 3 / 2 of the burst or inter-burst duration PDF. This property of stochastic processes might be used to detect spurious memory in various non-equilibrium systems, where observed macroscopic behavior can be derived from the imitative interactions of agents. View Full-Text
Keywords: spurious memory; non-equilibrium systems; agent-based modeling; stochastic modeling; Markov processes; first passage times spurious memory; non-equilibrium systems; agent-based modeling; stochastic modeling; Markov processes; first passage times
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Gontis, V.; Kononovicius, A. Spurious Memory in Non-Equilibrium Stochastic Models of Imitative Behavior. Entropy 2017, 19, 387.

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