Premium
Statistics for the contact process
Author(s) -
Fiocco Marta,
Van Zwet Willem R.
Publication year - 2002
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/1467-9574.00197
Subject(s) - contact process (mathematics) , estimator , supercritical fluid , constant (computer programming) , mathematics , process (computing) , infection rate , statistics , statistical physics , mathematical analysis , physics , computer science , thermodynamics , medicine , surgery , programming language , operating system
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 →∞