  We analyze the scaled voter model, which is a generalization of the noisy
voter model with time-dependent herding behavior. We consider the case when the
intensity of herding behavior grows as a power-law function of time. In this
case, the scaled voter model reduces to the usual noisy voter model, but it is
driven by the scaled Brownian motion. We derive analytical expressions for the
time evolution of the first and second moments of the scaled voter model. In
addition, we have derived an analytical approximation of the first passage time
distribution. By numerical simulation, we confirm our analytical results as
well as show that the model exhibits long-range memory indicators despite being
a Markov model. The proposed model has steady-state distribution consistent
with the bounded fractional Brownian motion, thus we expect it to be a good
substitute model for the bounded fractional Brownian motion.
