UNIFORM MODERATE DEVIATIONS OF FUNCTIONAL EMPIRICAL
PROCESSES OF MARKOV CHAINS
Abstract: We obtain uniform (in time) moderate deviations for the functional empirical
process of a general state space Markov chain under the geometric ergodicity assumption,
and a regularity condition for the initial measure, by the regeneration split chain
method. Our results deal both with bounded and unbounded class of functions.
1991 AMS Mathematics Subject Classification: Primary 60F10.
Key words and phrases: Moderate deviations; Markov chains; geometric ergodicity;
regeneration split chain method; functional empirical process.