Space-time estimation of a particle system model

Let X be a discrete time contact process (CP) on ?², as defined by Durrett and Levin (1994, Stochastic spatial models: a user's guide to ecological applications. Philosophical Transactions of the Royal Society of London Series B, 343, 329–350). We study the estimation of the model based on space-time evolution of X, that is, T + 1 successive observations of X on a finite subset S of sites. We consider the maximum marginal pseudo-likelihood (MPL) estimator and show that, when T→∞, this estimator is consistent and asymptotically normal for a non-vanishing supercritical CP. Numerical studies confirm these theoretical ones.