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Upper and Lower Bounds for Stochastic Processes - Decomposition Theorems (Hardcover, 2nd ed. 2021)
Loot Price: R4,913
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Upper and Lower Bounds for Stochastic Processes - Decomposition Theorems (Hardcover, 2nd ed. 2021)
Series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, 60
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This book provides an in-depth account of modern methods used to
bound the supremum of stochastic processes. Starting from first
principles, it takes the reader to the frontier of current
research. This second edition has been completely rewritten,
offering substantial improvements to the exposition and simplified
proofs, as well as new results. The book starts with a thorough
account of the generic chaining, a remarkably simple and powerful
method to bound a stochastic process that should belong to every
probabilist's toolkit. The effectiveness of the scheme is
demonstrated by the characterization of sample boundedness of
Gaussian processes. Much of the book is devoted to exploring the
wealth of ideas and results generated by thirty years of efforts to
extend this result to more general classes of processes,
culminating in the recent solution of several key conjectures. A
large part of this unique book is devoted to the author's
influential work. While many of the results presented are rather
advanced, others bear on the very foundations of probability
theory. In addition to providing an invaluable reference for
researchers, the book should therefore also be of interest to a
wide range of readers.
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