Parameter estimation for the supercritical contact process

Contact processes-and, more generally, interacting particle processes-can serve as models for a large variety of statistical problems, especially if we allow some simple modifications that do not essentially complicate the mathematical treatment of these processes. We begin a statistical study of the supercritical contact process that starts with a single infected site at the origin and is conditioned on survival of the infection. We consider the statistical problem of estimating the parameter lambda of the process on the basis of an observation of the process at a single time t. We propose an estimator of lambda and show that it is consistent and asymptotically normal as t --> infinity.