Before revision:  For an infinite-horizon model with linear state dynamics and exogenous volatilities,  the equilibrium returns mean-revert around their frictionless counterparts -- the deviation has Ornstein-Uhlenbeck dynamics for quadratic costs whereas it follows a doubly-reflected Brownian motion if costs are proportional.
After revision:  For an infinite-horizon model with linear state dynamics and exogenous volatilities, we prove that the equilibrium returns mean-revert around their frictionless counterparts -- the deviation has Ornstein-Uhlenbeck dynamics for quadratic costs whereas it follows a doubly-reflected Brownian motion if costs are proportional.