  The binary contact path process (BCPP) introduced in Griffeath (1983)
describes the spread of an epidemic on a graph and is an auxiliary model in the
study of improving upper bounds of the critical value of the contact process.
In this paper, we are concerned with the central limit theorem of the
occupation time of a normalized version of the BCPP (NBCPP) on a lattice. We
show that the centred occupation time process of the NBCPP converges in finite
dimensional distributions to a Brownian motion when the dimension of the
lattice and the infection rate of the model are sufficiently large and the
initial state of the NBCPP is distributed with a particular invariant
distribution.
