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Statistics for the contact process

Author

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  • Marta Fiocco
  • Willem R. Van Zwet

Abstract

A d‐dimensional contact process is a simplified model for the spread of an infection on the lattice Zd. At any given time t≥0, certain sites x∈Zd are infected while the remaining once are healthy. Infected sites recover at constant rate 1, while healthy sites are infected at a rate proportional to the number of infected neighboring sites. The model is parametrized by the proportionality constant λ. If λ is sufficiently small, infection dies out (subcritical process), whereas if λ is sufficiently large infection tends to be permanent (supercritical process). In this paper we study the estimation problem for the parameter λ of the supercritical contact process starting with a single infected site at the origin. Based on an observation of this process at a single time t, we obtain an estimator for the parameter λ which is consistent and asymptotically normal as t→∞

Suggested Citation

  • Marta Fiocco & Willem R. Van Zwet, 2002. "Statistics for the contact process," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 56(2), pages 243-251, May.
    • Handle: RePEc:bla:stanee:v:56:y:2002:i:2:p:243-251
    DOI: 10.1111/1467-9574.00197
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