Abstract
Chapter 1 describes the philosophy of the book and some of its highlights. For us a stochastic process is a collection of random variables (r.v.s) (X t ) t∈T , where T is an index set, and the goal of the book is to find upper bounds and lower bounds for the random quantity sup t∈T X t as a function of certain “geometric” characteristics. A fundamental example, which covers in particular the case of Gaussian processes is that of random series X t =∑ k≥1 ξ k f k (t), where f k are functions and ξ k are independent r.v.s. The study of such series occupies a large part of this book.
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Reference
Garsia, A.M., Rodemich, E., Rumsey, H.: A real variable lemma and the continuity of path of some Gaussian processes. Indiana Univ. Math. J. 20, 565–578 (1970/1971)
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Talagrand, M. (2014). Philosophy and Overview of the Book. In: Upper and Lower Bounds for Stochastic Processes. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, vol 60. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54075-2_1
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DOI: https://doi.org/10.1007/978-3-642-54075-2_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-54074-5
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