Anomalous diffusion : temporal non-Markovianity and weak ergodicitybreaking

2009
journal article
article
13
dc.abstract.enTraditionally, the discrimination between a Markovian and a non-Markovian process is based on the definition. If the process is Markovian, its transition probability does not depend on the history of the process and it fulfills the Smoluchowski-Chapman-Kolmogorov equation. A practical veri. cation of these two criteria is not always possible or fully conclusive. Therefore, we present an additional method which can be used to confirm the simplest version of Markovianity. This method is based on the properties of sums of independent random variables. We apply the presented method to prove the increment dependent character of an anomalous process combining long waiting times with long jumps. Such a process, despite being non-Markovian in nature, due to a competition between long waiting times and long jumps, can reveal `normal' behavior. We also demonstrate that this anomalous process breaks the ergodicity in the weak sense. Finally, we apply the suggested method to some experimental time series proving their Markovian nature for small timescales.pl
dc.affiliationWydział Fizyki, Astronomii i Informatyki Stosowanej : Instytut Fizyki im. Mariana Smoluchowskiegopl
dc.contributor.authorDybiec, Bartłomiej - 102110 pl
dc.date.accessioned2018-04-11T12:59:19Z
dc.date.available2018-04-11T12:59:19Z
dc.date.issued2009pl
dc.description.number8pl
dc.description.volume2009pl
dc.identifier.articleidP08025pl
dc.identifier.doi10.1088/1742-5468/2009/08/P08025pl
dc.identifier.eissn1742-5468pl
dc.identifier.urihttps://ruj.uj.edu.pl/xmlui/handle/item/53264
dc.languageengpl
dc.language.containerengpl
dc.rightsDodaję tylko opis bibliograficzny*
dc.rights.licencebez licencji
dc.rights.uri*
dc.subtypeArticlepl
dc.titleAnomalous diffusion : temporal non-Markovianity and weak ergodicitybreakingpl
dc.title.journalJournal of Statistical Mechanicspl
dc.typeJournalArticlepl
dspace.entity.typePublication
dc.abstract.enpl
Traditionally, the discrimination between a Markovian and a non-Markovian process is based on the definition. If the process is Markovian, its transition probability does not depend on the history of the process and it fulfills the Smoluchowski-Chapman-Kolmogorov equation. A practical veri. cation of these two criteria is not always possible or fully conclusive. Therefore, we present an additional method which can be used to confirm the simplest version of Markovianity. This method is based on the properties of sums of independent random variables. We apply the presented method to prove the increment dependent character of an anomalous process combining long waiting times with long jumps. Such a process, despite being non-Markovian in nature, due to a competition between long waiting times and long jumps, can reveal `normal' behavior. We also demonstrate that this anomalous process breaks the ergodicity in the weak sense. Finally, we apply the suggested method to some experimental time series proving their Markovian nature for small timescales.
dc.affiliationpl
Wydział Fizyki, Astronomii i Informatyki Stosowanej : Instytut Fizyki im. Mariana Smoluchowskiego
dc.contributor.authorpl
Dybiec, Bartłomiej - 102110
dc.date.accessioned
2018-04-11T12:59:19Z
dc.date.available
2018-04-11T12:59:19Z
dc.date.issuedpl
2009
dc.description.numberpl
8
dc.description.volumepl
2009
dc.identifier.articleidpl
P08025
dc.identifier.doipl
10.1088/1742-5468/2009/08/P08025
dc.identifier.eissnpl
1742-5468
dc.identifier.uri
https://ruj.uj.edu.pl/xmlui/handle/item/53264
dc.languagepl
eng
dc.language.containerpl
eng
dc.rights*
Dodaję tylko opis bibliograficzny
dc.rights.licence
bez licencji
dc.rights.uri*
dc.subtypepl
Article
dc.titlepl
Anomalous diffusion : temporal non-Markovianity and weak ergodicitybreaking
dc.title.journalpl
Journal of Statistical Mechanics
dc.typepl
JournalArticle
dspace.entity.type
Publication
Affiliations

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