Bl. Granovsky et L. Rozov, ON TRANSIENT-BEHAVIOR OF A NEAREST-NEIGHBOR BIRTH-DEATH PROCESS ON A LATTICE, Journal of Applied Probability, 31(2), 1994, pp. 549-553
We provide the explicit expression for the mean coverage function of a
generalized voter model on a regular lattice and establish a characte
rization of the class of the above processes. As a result, we derive t
he exact rate of convergence of the considered processes to the steady
state. We also prove the existence of different processes with the sa
me mean coverage function on a given lattice.