ABSTRACT
This chapter establishes the large deviations principle for two special classes of jump processes. The flat boundary process is a jump Markov process, except that it is restricted to a half-space. The method of analysis is similar for both types of processes, and so the theories are developed together as much as possible. The analysis is an extension of the arguments given in Chapter 5. The chapter also establishes some properties of the rate functions, derive the upper bound for the processes that consist essentially of checking that the same steps are valid. It then establishes some facts about constant coefficient jump Markov processes, including Kurtz’s Theorem for the constant coefficient case, and conclude with proofs of the lower bounds and Kurtz’s Theorem for the two types of processes. A flat boundary process would seem to be a limit of finite levels processes as the number of levels becomes infinite.
