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Titlebook: Random Fields and Geometry; Robert J. Adler,Jonathan E. Taylor Book 2007 Springer-Verlag New York 2007 Area.Gaussian process.Volume.astrop

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書目名稱Random Fields and Geometry
編輯Robert J. Adler,Jonathan E. Taylor
視頻videohttp://file.papertrans.cn/822/821044/821044.mp4
概述Recasts old topics in random fields by following a completely new way of handling both geometry and probability.Significant exposition of the work of others in the field.Excellent reference work as we
叢書名稱Springer Monographs in Mathematics
圖書封面Titlebook: Random Fields and Geometry;  Robert J. Adler,Jonathan E. Taylor Book 2007 Springer-Verlag New York 2007 Area.Gaussian process.Volume.astrop
描述Since the term “random ?eld’’ has a variety of different connotations, ranging from agriculture to statistical mechanics, let us start by clarifying that, in this book, a random ?eld is a stochastic process, usually taking values in a Euclidean space, and de?ned over a parameter space of dimensionality at least 1. Consequently, random processes de?ned on countable parameter spaces will not 1 appear here. Indeed, even processes on R will make only rare appearances and, from the point of view of this book, are almost trivial. The parameter spaces we like best are manifolds, although for much of the time we shall require no more than that they be pseudometric spaces. With this clari?cation in hand, the next thing that you should know is that this book will have a sequel dealing primarily with applications. In fact, as we complete this book, we have already started, together with KW (Keith Worsley), on a companion volume [8] tentatively entitled RFG-A,or Random Fields and Geometry: Applications. The current volume—RFG—concentrates on the theory and mathematical background of random ?elds, while RFG-A is intended to do precisely what its title promises. Once the companion volume is publ
出版日期Book 2007
關鍵詞Area; Gaussian process; Volume; astrophysics; differential geometry; geometry; probability
版次1
doihttps://doi.org/10.1007/978-0-387-48116-6
isbn_softcover978-1-4419-2369-1
isbn_ebook978-0-387-48116-6Series ISSN 1439-7382 Series E-ISSN 2196-9922
issn_series 1439-7382
copyrightSpringer-Verlag New York 2007
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沙發(fā)
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地板
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Integral GeometryOur aim in this chapter is to develop a framework for handling ., which we now redefine in a nonstochastic framework.
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Random Fields on ManifoldsIn essence, this chapter will repeat, for random fields on manifolds, what we have already achieved in the Euclidean setting.
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Mean Intrinsic VolumesIn the preceding two chapters we devoted a considerable amount of energy to computing the mean Euler characteristics of the excursion sets of smooth Gaussian fields. However, we know from both Chapters 6 and 7 that the Euler characteristic is but one of the family of geometric quantifiers known as the Lipschitz–Killing curvatures.
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Non-Gaussian GeometryThis final chapter is, for two reasons, somewhat of an outlier as far as this book is concerned.
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