- Large deviation upper bound and its application to measure valued processes

The objective of present chapter is to discuss the large deviation upper bound on a class of metric space and try to find general conditions for getting the upper bound. The motivation for this research is to study the large deviation of a class of measure valued-Markov processes discussed. It turns out that in this situation the upper bound is the most difficult part in establishing the large deviation principle. A detailed discussion is given about several kinds of measurability for the space of measure-valued cadlag paths satisfying certain moment condition.