Maximum likelihood for the fully observed contact process. (English) Zbl 1073.62069

Summary: The contact process – and more generally, interacting particle systems – are useful and interesting models for a variety of statistical problems. This paper is concerned with maximum likelihood estimation of the parameters of the process for the case where the process is supercritical, starts with a single infected site at the origin and is observed during a long time interval \([0,t]\). We construct the estimators and prove their consistency and asymptotic normality as \(t\rightarrow \infty\). We also discuss the relation with the estimation problem for the process observed at a single large time.


62M09 Non-Markovian processes: estimation
60K35 Interacting random processes; statistical mechanics type models; percolation theory
62M30 Inference from spatial processes
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