Spurious Memory in Non-Equilibrium Stochastic Models of Imitative Behavior
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 pro...
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| Format: | Article |
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MDPI AG
2017-07-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/19/8/387 |
| _version_ | 1798006158245494784 |
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| author | Vygintas Gontis Aleksejus Kononovicius |
| author_facet | Vygintas Gontis Aleksejus Kononovicius |
| author_sort | Vygintas Gontis |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-11T12:50:34Z |
| format | Article |
| id | doaj.art-3e1409ed77d64c18be3b881ea1721bd3 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T12:50:34Z |
| publishDate | 2017-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-3e1409ed77d64c18be3b881ea1721bd32022-12-22T04:23:13ZengMDPI AGEntropy1099-43002017-07-0119838710.3390/e19080387e19080387Spurious Memory in Non-Equilibrium Stochastic Models of Imitative BehaviorVygintas Gontis0Aleksejus Kononovicius1Institute of Theoretical Physics and Astronomy, Vilnius University, Saulėtekio al. 3, 10257 Vilnius, LithuaniaInstitute of Theoretical Physics and Astronomy, Vilnius University, Saulėtekio al. 3, 10257 Vilnius, LithuaniaThe 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.https://www.mdpi.com/1099-4300/19/8/387spurious memorynon-equilibrium systemsagent-based modelingstochastic modelingMarkov processesfirst passage times |
| spellingShingle | Vygintas Gontis Aleksejus Kononovicius Spurious Memory in Non-Equilibrium Stochastic Models of Imitative Behavior Entropy spurious memory non-equilibrium systems agent-based modeling stochastic modeling Markov processes first passage times |
| title | Spurious Memory in Non-Equilibrium Stochastic Models of Imitative Behavior |
| title_full | Spurious Memory in Non-Equilibrium Stochastic Models of Imitative Behavior |
| title_fullStr | Spurious Memory in Non-Equilibrium Stochastic Models of Imitative Behavior |
| title_full_unstemmed | Spurious Memory in Non-Equilibrium Stochastic Models of Imitative Behavior |
| title_short | Spurious Memory in Non-Equilibrium Stochastic Models of Imitative Behavior |
| title_sort | spurious memory in non equilibrium stochastic models of imitative behavior |
| topic | spurious memory non-equilibrium systems agent-based modeling stochastic modeling Markov processes first passage times |
| url | https://www.mdpi.com/1099-4300/19/8/387 |
| work_keys_str_mv | AT vygintasgontis spuriousmemoryinnonequilibriumstochasticmodelsofimitativebehavior AT aleksejuskononovicius spuriousmemoryinnonequilibriumstochasticmodelsofimitativebehavior |