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Summary: Level sets and extrema of random processes and fields.
Jean-Marc Aza¨is
Mario Wschebor
Universit´e de Toulouse UPS CNRS : Institut de Math´ematiques Laboratoire
de Statistiques et Probabilit´es 118 Route de Narbonne, 31062 Toulouse cedex 09,
France
Centro de Matem´atica. Facultad de Ciencias., Universidad de la Rep´ublica.,
Calle Igu´a 4225. 11400 Montevideo. Uruguay.
E-mail address: azais@cict.fr
E-mail address: wschebor@cmat.edu.uy
Contents
Introduction 5
Reading diagram 12
Chapter 1. Classical results on the regularity of the paths. 15
1. Kolmogorov's Extension Theorem. 15
2. Reminder on the Normal Distribution. 17
3. 0-1 law for Gaussian processes. 20
4. Regularity of the paths. 22
Exercises 34
Chapter 2. Basic Inequalities for Gaussian Processes 39
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