Parameter estimation for the supercritical contact process

Marta Fiocco, Willem R. Van Zwet
2003 Bernoulli  
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
more » ... A of the process on the basis of an observation of the process at a single time t. We propose an estimator of A and show that it is consistent and asymptotically normal as t --> oo . {£) 0 } : t:;::. 0} will denote the processes starting with every site infected, or with a single infected site at the origin. If the starting set is chosen at random according to a probability distribution a, then the process will be written as { £~ : t :;::. 0} . If we do not want to specify the initial state of the process at all, we simply write g 1 : t :;::. 0}. We also need a compact notation for the state of a single site x E 7l.d at time t. For any contact process s 1, we write if x is healthy at time t, (1.1) thus using the same symbol £1 for both the set of infected points and its indicator function. Of course s:(x) and s~(x) will refer to the processes £1 and s~ in the same manner.
doi:10.3150/bj/1072215201 fatcat:acrjnpnsgnht3fcwqbvlx7snjm