Large deviation theorems at the Donsker-Varadhan level-three type are established for certain classes of stationary processes. Proceeding from more general to more specific assumptions allows us to describe the rate function more explicitly.
"Large Deviation Principles for Stationary Processes." Ann. Probab. 16 (4) 1481 - 1495, October, 1988. https://doi.org/10.1214/aop/1176991579