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.

Frequency of symbol occurrences in simple non-primitive stochastic models / D. DE FALCO, M. GOLDWURM, V. LONATI (LECTURE NOTES IN COMPUTER SCIENCE). - In: Developments in Language Theory / [a cura di] Z. Esik, Z. Fulop. - Berlin : Springer-Verlag, 2003. - ISBN 3540404341. - pp. 242-253 (( Intervento presentato al 7. convegno DLT tenutosi a Szeged nel 2003.

### Frequency of symbol occurrences in simple non-primitive stochastic models

#### 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.
##### Scheda breve Scheda completa Scheda completa (DC) Stochastic Mode;l Limit Distribution; Nonnegative Matrix; Asymptotic Evaluation; Approximate String Match
Settore INF/01 - Informatica
Settore MAT/06 - Probabilita' e Statistica Matematica
2003
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/2434/4960`
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