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Random Fields and Geometry

Robert J. Adler Jonathan E. Taylor

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Institución detectada Año de publicación Navegá Descargá Solicitá
No detectada 2007 SpringerLink

Información

Tipo de recurso:

libros

ISBN impreso

978-0-387-48112-8

ISBN electrónico

978-0-387-48116-6

Editor responsable

Springer Nature

País de edición

Reino Unido

Fecha de publicación

Información sobre derechos de publicación

© Springer New York 2007

Cobertura temática

matematica

Matemáticas

fisica

Ciencias físicas

Tabla de contenidos

doi: 10.1007/978-0-387-48116-6_11

Random Fields on Euclidean Spaces

Robert J. Adler; Jonathan E. Taylor

The main result of this chapter is Theorem 11.7.2 and its corollaries, which give explicit formulas for the mean Euler characteristic of the excursion sets of smooth Gaussian fields over rectangles in ℝ.

Part III - The Geometry of Random Fields | Pp. 263-299

doi: 10.1007/978-0-387-48116-6_12

Random Fields on Manifolds

Robert J. Adler; Jonathan E. Taylor

In essence, this chapter will repeat, for random fields on manifolds, what we have already achieved in the Euclidean setting.

Part III - The Geometry of Random Fields | Pp. 301-330

doi: 10.1007/978-0-387-48116-6_13

Mean Intrinsic Volumes

Robert J. Adler; Jonathan E. Taylor

In 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.

Part III - The Geometry of Random Fields | Pp. 331-348

doi: 10.1007/978-0-387-48116-6_14

Excursion Probabilities for Smooth Fields

Robert J. Adler; Jonathan E. Taylor

As we have mentioned more than once before, one of the oldest and most important problems in the study of stochastic processes of any kind is to evaluate the where is a random process over some parameter set . As usual, we shall restrict ourselves to the case in which is centered and Gaussian and is compact for the canonical metric of (1.3.1).

Part III - The Geometry of Random Fields | Pp. 349-386

doi: 10.1007/978-0-387-48116-6_15

Non-Gaussian Geometry

Robert J. Adler; Jonathan E. Taylor

This final chapter is, for two reasons, somewhat of an outlier as far as this book is concerned.

Part III - The Geometry of Random Fields | Pp. 387-433