## 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.

### MSC:

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

 [1] Fiocco, M.; van Zwet, W.R., Decaying correlations for the supercritical contact process conditioned on survival, Bernoulli, 9, 5, 763-781, (2003) · Zbl 1054.60103 [2] Fiocco, M.; van Zwet, W.R., Parameter estimation for the supercritical contact process, Bernoulli, 9, 6, 1071-1092, (2003) · Zbl 1052.62087 [3] M. Fiocco, W.R. van Zwet, Maximum likelihood estimation for the contact process, Festschrift for Herman Rubin, Institute of Mathematical Statistics Lecture Notes-Monograph Series, vol. 45, 2004, pp. 309-318. · Zbl 1268.62102 [4] Harris, T.E., Contact interaction on a lattice, Ann. probab., 2, 969-988, (1974) · Zbl 0334.60052 [5] Liggett, T., Interacting particle systems, (1985), Springer Heidelberg, New York · Zbl 0559.60078 [6] Liggett, T., Stochastic interacting systems: contact, voter and exclusion processes, (1999), Springer Heidelberg, New York · Zbl 0949.60006 [7] Shorack, G.R., Probability for statisticians, (2000), Springer Heidelberg, New York · Zbl 0951.62005
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