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Stochastic Models of Evolution

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Extracting Knowledge From Time Series

Part of the book series: Springer Series in Synergetics ((SSSYN))

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Abstract

To continue the discussion of randomness given in Sect. 2.2.1, we briefly touch on stochastic models of temporal evolution (random processes). They can be specified either via explicit definition of their statistical properties (probability density functions, correlation functions, etc., Sects. 4.1, 4.2 and 4.3) or via stochastic difference or differential equations. Some of the most widely known equations, their properties and applications are discussed in Sects. 4.4 and 4.5.

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Notes

  1. 1.

    There is also another terminology where equation (4.3) is called an auto-correlation function, and after the normalisation, a normalised auto-correlation function. To avoid misunderstanding, we do not use it in this book.

  2. 2.

    There is also somewhat different interpretation related to an additional requirement of a finite variance for a weakly stationary process. In such a case, the weak stationarity does not follow from the strong one.

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Authors and Affiliations

  1. Saratov State University, Astrakhanskaya Street 83, 410012, Saratov, Russia

    Prof. Boris P. Bezruchko

  2. Russian Academy of Science, V.A. Kotel’nikov Institute of RadioEngineering and Electronics, Saratov Branch, Zelyonaya Str. 38, 410019, Saratov, Russia

    Dr. Dmitry A. Smirnov

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  1. Prof. Boris P. Bezruchko
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  2. Dr. Dmitry A. Smirnov
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Correspondence to Boris P. Bezruchko .

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Bezruchko, B.P., Smirnov, D.A. (2010). Stochastic Models of Evolution. In: Extracting Knowledge From Time Series. Springer Series in Synergetics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12601-7_4

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  • DOI: https://doi.org/10.1007/978-3-642-12601-7_4

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