An introduction to large deviations

WS 2020/21


Lectures and Tutorial classes: Tuesday 10:15 - 11:45 and Thursday 14:15 - 15:45 Online, link to Zoom

Office hours: Thursday 16:00 - 17:30, Online, link to Zoom (different from course link)


Course in the Moodle system: link



TOPICS


  • Cramer's theorem;
  • Sanov's theorem;
  • Notion of large deviation principle;
  • Exponential tightness and weak LDP
  • Contraction principle;
  • Schilder's theorem (LDP for Brownian motion);
  • Friedlin-Wentzell theory (LDP for SDE);
  • Varadhan's lemma;
  • Exponential equivalence;
  • Application of LDP


    • LITERATURE


  • Frank den Hollander. "Large deviations"
  • Olav Kallenberg "Foundations of modern probability" 2002, Second Edition
  • Peter Mörters "Large deviation theory and applications"
  • Scott Robertson "Large Deviation Principles"
  • 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"


    • LECTURE NOTES


    Notes



    PROBLEM SHEETS


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