Asymptotics of Continuous Bayes for Non-i.i.d. Sources
  Clarke and Barron analysed the relative entropy between an i.i.d. source and a Bayesian mixture over a continuous class containing that source. In this paper a comparable result is obtained when the source is permitted to be both non-stationary and dependent. The main theorem shows that Bayesian methods perform well for both compression and sequence prediction even in this most general setting with only mild technical assumptions. 
Tor Lattimore and Marcus Hutter
cs.IT math.IT