ABSTRACT
This chapter can be viewed as a guided tour through basic large deviations. Following a heuristic exposition, the authors derive large deviations estimates for random variables. They provide proofs when these provide insight, or are typical; otherwise, they provide references. To motivate the exponential form of the large deviations estimates, the authors discuss a few examples. One such example has more than purely theoretical or pedagogical interest; it has monetary applications. The authors also present some simple calculations in order to develop a feeling for the scope of the large deviations estimates. There are a few cases where the full asymptotic expansion has been worked out, and there are many more cases where some formal terms have been calculated.
