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Frequency of Symbol Occurrences in Simple Non-primitive Stochastic Models

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Developments in Language Theory (DLT 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2710))

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Abstract

We study the random variable Y n representing the number of occurrences of a given symbol in a word of length n generated at random. The stochastic model we assume is a simple non-ergodic model defined by the product of two primitive rational formal series, which form two distinct ergodic components. We obtain asymptotic evaluations for the mean and the variance of Y n and its limit distribution. It turns out that there are two main cases: if one component is dominant and non-degenerate we get a Gaussian limit distribution; if the two components are equipotent and have different leading terms of the mean, we get a uniform limit distribution. Other particular limit distributions are obtained in the case of a degenerate dominant component and in the equipotent case when the leading terms of the expectation values are equal.

This work has been supported by the Project M.I.U.R. COFIN “Formal languages and automata: theory and applications”.

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Author information

Authors and Affiliations

  1. Dipartimento di Scienze dell’Informazione, Università degli Studi di Milano, via Comelico 39, 20135, Milano, Italy

    Diego de Falco, Massimiliano Goldwurm & Violetta Lonati

Authors
  1. Diego de Falco
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  2. Massimiliano Goldwurm
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  3. Violetta Lonati
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Editor information

Editors and Affiliations

  1. Department of Informatics, University of Szeged, Árpád tér 2, 6720, Szeged, Hungary

    Zoltán Ésik  & Zoltán Fülöp  & 

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de Falco, D., Goldwurm, M., Lonati, V. (2003). Frequency of Symbol Occurrences in Simple Non-primitive Stochastic Models. In: Ésik, Z., Fülöp, Z. (eds) Developments in Language Theory. DLT 2003. Lecture Notes in Computer Science, vol 2710. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45007-6_19

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  • DOI: https://doi.org/10.1007/3-540-45007-6_19

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  • Print ISBN: 978-3-540-40434-7

  • Online ISBN: 978-3-540-45007-8

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