Statistics for the contact process

A d ‐dimensional contact process is a simplified model for the spread of an infection on the lattice Z d . At any given time t ≥ 0 , certain sites x ∈ Z d 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 →∞