LARGE DEVIATIONS AND STRONG MIXING

The Large Deviation Principle (LDP) with respect to the tau-topology h olds for the empirical measure of any alpha-mixing or any phi-mixing s tationary process with a hyper-exponential mixing rate of at least alp ha(n) much less than exp(-n(log n)(1+delta)), for some delta > 0 or at least phi(n) much less than exp(-nl(n)) with l(n) --> infinity. Posit ive recurrent Doeblin Markov chain examples for which the LDP does not hold demonstrate the tightness of these rates and the relationship be tween the LDP for the empirical means of all bounded R(d)-valued funct ionals and the LDP for the empirical measure.