Continuous dependence of ergodic limits

The discrete and continuous parameter forms of the mean ergodic theorem conclude that as N --> [infinity] or [tau] --> [infinity]. The ergodic limit P is shown to depend continuously on the operator T in the discrete case or on the infinitesimal generator A of the semigroup T in the continuous case. These results are motivated by recent investigations into the asymptotics of Markov chains.mean ergodic theorems Markov chains Markov processes continuous dependence ergodic limits