Large deviation theory is a part of probability theory that
deals with the description of events where a sum of random
variables deviates from its mean by more than a “normal”
amount, i.e., beyond what is described by the central limit
theorem. A precise calculation of the probabilities of such
events turns out to be crucial for the study of integrals
of exponential functionals of random variables, which come
up in a variety of different contexts. Large deviation
theory finds application in probability theory, statistics,
operations research, ergodic theory, information theory,
statistical physics, financial mathematics, and beyond. As such it is a very central area of mathematics.
Prerequisite
<td valign="\"top\""></td><td valign="\"top\"">Inleiding kansrekening</td>### Literature
Frank den Hollander, Large Deviations, Fields Institute Monographs 14, American Mathematical Society, Providence, Rhode Island, 2000 (ISBN 0-8218-1989-5)
The book consists of two parts:
Part A (Chapters I-V): Theory. Part B (Chapters VI-X): Applications.
Content:
Chapters I-II: Large deviations for i.i.d. random sequences.
Chapter III: General theory.
Chapter IV: Large deviations for Markov sequences.
Chapter V: Large deviations or non-i.i.d. random sequences.
Chapter VI: Statistical hypothesis testing.
Chapter VII: Random walk in random environment.
Chapter VIII: Heat conduction with random sources and sinks.
Chapter IX: Polymer chains.
Chapter X: Interacting diffusions.
During the course, most of Part A will be covered and a selection will be made from Part B.
The book also contains a large number of exercises, whose solutions are presented in an appendix.
Examination
Oral