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Stein's method for normal approximation of random variables
 Strnad, Martin ; Kříž, Pavel (advisor) ; Nagy, Stanislav (referee)
The Stein's method is a collection of probabilistic techniques for answering the ques- tion as to how far the probability distributions of random variables are from each other. This thesis only concerns the basics of the approach. We use the Kolmogorov distance and the total variation distance to formalize the concept of the distance between mea- sures. We focus on the normal distribution for which we first find a suitable differential operator, often called Stein operator, that bears much information. Not only does it charactize the Gaussian measure, it also gives us a means to quantify the distance from another random variable's distribution. Finally, we apply the method to prove the clas- sic Berry-Esseen inequality for a sum of independent and identically distributed random variables. 1
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