The Geometry of Random Fields
The Geometry of Random Fields
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USDOriginally published in 1981, The Geometry of Random Fields remains an important text for its coverage and exposition of the theory of both smooth and non-smooth 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. The Geometry of Random Fields is essential reading for 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.
- Self-contained classic text on the theory of smooth and non-smooth random fields
- Accessible to readers who are specialists in neither probability nor geometry
- Covers both smooth and non-smooth fields, whereas other books on the subject tend to treat only one of the two scenarios
Product details
January 2010Paperback
9780898716931
184 pages
230 × 152 × 19 mm
0.484kg
This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
Table of Contents
- Preface to the Classics edition
- Preface
- Corrections and comments
- 1. Random fields and excursion sets
- 2. Homogeneous fields and their spectra
- 3. Sample function regularity
- 4. Geometry and excursion characteristics
- 5. Some expectations
- 6. Local maxima and high-level excursions
- 7. Some non-Gaussian fields
- 8. Sample function erraticism and Hausdorff dimension
- Appendix. The Markov property for Gaussian fields
- References
- Author index
- Subject index.
