# The Deterministic Limit of the Moran Model: a Uniform Central Limit Theorem

Cordero F (2017)
MARKOV PROCESSES AND RELATED FIELDS 23(2): 313-324.

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
Abstract / Bemerkung
We consider a Moran model with two allelic types, mutation and selection. In this work, we study the behaviour of the proportion of fit individuals when the size of the population tends to infinity, without any rescaling of parameters or time. We first prove that the latter converges, uniformly in compacts in probability, to the solution of an ordinary differential equation, which is explicitly solved. Next, we study the stability properties of its equilibrium points. Moreover, we show that the fluctuations of the proportion of fit individuals, after a proper normalisation, satisfy a uniform central limit theorem in [0, infinity). As a consequence, we deduce the convergence of the corresponding stationary distributions.
Stichworte
Erscheinungsjahr
Zeitschriftentitel
MARKOV PROCESSES AND RELATED FIELDS
Band
23
Zeitschriftennummer
2
Seite
313-324
ISSN
PUB-ID

### Zitieren

Cordero F. The Deterministic Limit of the Moran Model: a Uniform Central Limit Theorem. MARKOV PROCESSES AND RELATED FIELDS. 2017;23(2):313-324.
Cordero, F. (2017). The Deterministic Limit of the Moran Model: a Uniform Central Limit Theorem. MARKOV PROCESSES AND RELATED FIELDS, 23(2), 313-324.
Cordero, F. (2017). The Deterministic Limit of the Moran Model: a Uniform Central Limit Theorem. MARKOV PROCESSES AND RELATED FIELDS 23, 313-324.
Cordero, F., 2017. The Deterministic Limit of the Moran Model: a Uniform Central Limit Theorem. MARKOV PROCESSES AND RELATED FIELDS, 23(2), p 313-324.
F. Cordero, “The Deterministic Limit of the Moran Model: a Uniform Central Limit Theorem”, MARKOV PROCESSES AND RELATED FIELDS, vol. 23, 2017, pp. 313-324.
Cordero, F.: The Deterministic Limit of the Moran Model: a Uniform Central Limit Theorem. MARKOV PROCESSES AND RELATED FIELDS. 23, 313-324 (2017).
Cordero, Fernando. “The Deterministic Limit of the Moran Model: a Uniform Central Limit Theorem”. MARKOV PROCESSES AND RELATED FIELDS 23.2 (2017): 313-324.

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