Limiting behavior of a random variable conditional on a rare event

Bachelor thesis (2020)

Authors

K. Zomerdijk Electrical Engineering, Mathematics and Computer Science

Contributors

R.C. Kraaij Applied Probability - EEMCS (mentor)
Y. van Gennip Mathematical Physics - EEMCS (graduation committee member)
Faculty
Electrical Engineering, Mathematics and Computer Science, Electrical Engineering, Mathematics and Computer Science
Copyright: © 2020 Koen Zomerdijk
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Published Date

30-07-2020

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Abstract

As an insurer you want identify the risks you take to prevent bankruptcy. The
theory of large deviations formalizes the study of such rare events. We will use the
theorem of Cramér, which is a main theorem in large deviation theory, to investigate
the rate at which the probability of large deviations of the sums of random variables
decay. Using Sanov’s theorem we will derive an expression for large deviations of
the empirical measure. Furthermore, we will use Gibbs’s principle to derive the
distribution of random variables conditional on a large deviation.

Files

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