ABSTRACT
This chapter describes several processes, starting with the standard and simple and proceeding to the less so. We introduce large deviations for processes. The results of Chapter 1 are applied to analyze these processes. In particular, a slight modification of the proof of the upper bound in Chernoff’s Theorem is used. Applications of the current results are presented in Chapter 10. The results of this chapter are needed only for Chapter 10; however, they serve as a simple introduction to large deviations for processes. The general derivation provided in Chapter 5 is far more involved. To analyze the random walk, we need only to incorporate the starting position x 0. A standard branching process, also called a Galton-Watson process, is also defined.
