Limiting behavior of a random variable conditional on a rare event

Limiting behavior of a random variable conditional on a rare event

Zomerdijk, Koen (TU Delft Electrical Engineering, Mathematics and Computer Science)

Kraaij, R.C. (mentor)
van Gennip, Y. (graduation committee)

Delft University of Technology

Applied Mathematics

2020-07-30

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.

large deviation
rate function
rare event

http://resolver.tudelft.nl/uuid:92cd3100-053d-482d-a159-543fd6681220

Student theses

bachelor thesis

© 2020 Koen Zomerdijk