An introduction to large deviations
Winter Semester 2020/21
Lectures and Tutorial classes: Tue 10:15–11:45 am and Thu 2:15–3:45 pm Online, link to Zoom
Office hours: Thu 4:00–5:30 pm, Online, link to Zoom (different from course link)
Course in the Moodle system
Topics
- Cramer's theorem
- Notion of large deviation principle
- Contraction principle
- Schilder's theorem (LDP for Brownian motion)
- Friedlin-Wentzell theory (LDP for SDE)
- Gärtner-Ellis's theorem
- Varadhan's lemma
- Exponential tightness and weak LDP
- Application of LDP
Literature
- Frank den Hollander “Large deviations” (PDF)
- Olav Kallenberg “Foundations of modern probability” 2002, Second Edition
- Peter Mörters “Large deviation theory and applications” (PDF)
- Scott Robertson “Large Deviation Principles” (PDF)
- Amir Dembo and Ofer Zeitouni “Large deviations techniques and applications”
- Firas Rassoul-Agha and Timo Seppäläinen “A course on large deviations with an introduction to Gibbs measures”