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Space-time estimation of a particle system model. (Estimation spatio-temporelle d’un modèle de système de particules.) (French) Zbl 1061.62126

Summary: Let \(X\) be a discrete time contact process (CP) on \(\mathbb Z^2\) as defined by R. Durrett and S. A. Levin [Phil. Trans. R. Soc. London, Ser. B 343, 329–350 (1994); see also SIAM Rev. 41, No. 4, 677–718 (1999; Zbl 0940.60086)]. We study the estimation of the model based on space-time evolution of \(X\), that is, \(T+1\) successive observations of \(X\) on a finite subset \(S\) of sites. We consider the maximum marginal pseudo-likelihood (MPL) estimator and show that, when \(T\to \infty\), this estimator is consistent and asymptotically normal for a non vanishing supercritical CP.

MSC:

62M09 Non-Markovian processes: estimation
62F12 Asymptotic properties of parametric estimators

Citations:

Zbl 0940.60086
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References:

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