The Geometry of Random Fields (In Applied Mathematics)
English | 2010 | ISBN: 0898716934 | 302 Pages | DJVU | 2.75 MB
Originally published in 1981, The Geometry of Random Fields remains an important text for its coverage and exposition of the theory of both smooth and nonsmooth random fields; closed form expressions for various geometric characteristics of the excursion sets of smooth, stationary, Gaussian random fields over N-dimensional rectangles; descriptions of the local behavior of random fields in the neighborhoods of high maxima; and a treatment of the Markov property for Gaussian fields.
Audience: The core audience of the book is researchers in probability and statistics, with no prior knowledge of geometry required. Since the book was originally published it has become a standard reference in areas of physical oceanography, cosmology, and neuroimaging. It is written at a level accessible to nonspecialists, including advanced undergraduates and early graduate students.
Contents: Preface to the Classics Edition; Preface; Corrections and Comments; Chapter 1: Random Fields and Excursion Sets; Chapter 2: Homogeneous Fields and Their Spectra; Chapter 3: Sample Function Regularity; Chapter 4: Geometry and Excursion Characteristics; Chapter 5: Some Expectations; Chapter 6: Local Maxima and High-Level Excursions; Chapter 7: Some Non-Gaussian Fields; Chapter 8: Sample Function Erraticism and Hausdorff Dimension; Appendix: The Markov Property for Gaussian Fields; References; Author Index; Subject Index.