Large deviations: From empirical mean and measure to partial sums process

The large deviation principle is known to hold for the empirical measures (occupation times) of Polish space valued random variables and for the empirical means of Banach space valued random variables under Markov dependence or mixing conditions, and subject to the appropriate exponential tail conditions. It is proved here that these conditions suffice for the large deviation principle to carry over to the partial sums process corresponding to these objects. As demonstrated, this result yields the large deviations of the cost-sampled empirical distribution and is also relevant in studying the buildup of delays in queuing networks.