Journal of Statistical Physics, Vol. 117, Nos. 5/6, December 2004. p. 845-889.
We obtain an upper large deviations bound which shows that for some models of probabilistic cellular automata (which are far away from the product case) the lower large deviation bound derived in Eizenberg and Kifer J. Stat. Phys. 108: 1255-1280 (2002) is sharp, and so the corresponding large deviations phenomena cannot be described via the traditional Donsker-Varadhan form of the action functional. For models which are close to the product case we derive approximate large deviations bounds using the Donsker-Varadhan functional for the product case.