Transcription of Probability Theory: The Coupling Method - Universiteit …
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Probability Theory: The Coupling Method - Universiteit …
Probability theory : The Coupling Method Frank den Hollander Mathematical Institute, Leiden University, Box 9512, 2300 RA Leiden, The Netherlands email: First draft: June 2010, LATEX-file prepared by H. Nooitgedagt. Second draft: September 2012, figures prepared by A. Troiani. Third draft: December 2012. 1. ABSTRACT. Coupling is a powerful Method in Probability theory through which random variables can be compared with each other. Coupling has been applied in a broad variety of contexts, to prove limit theorems, to derive inequalities, or to obtain approximations. The present course is intended for master students and PhD students. A basic knowledge of Probability theory is required, as well as some familiarity with measure theory . The course first explains what Coupling is and what general framework it fits into. After that a number of applications are described.
1 Introduction In Sections 1.1–1.3 we describe three examples of coupling illustrating both the method and its usefulness. Each of these examples will be worked out in more detail later.
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