Introduction of the Large Deviation Principle

Abstract

In this chapter, we introduce the large deviation principle that is needed for further development in this book. For a sequence of i.i.d. random variable {X_n,n >1}, it is known from the strong law of large numbers that its empirical average converges to its mean almost surely, i.e.,

$$\frac{1}{n}\sum\limits_{i = 1}^n {{X_i} \to E\left[ {{X_1}} \right]} {a_\cdot}{s_\cdot}$$

(8.1)