Probability Theory: The Coupling Method - Universiteit …

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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.

  Methods, Theory, Probability, Coupling, Probability theory, The coupling method