Preface -- Part I. Gaussian Processes. Gaussian Fields. Gaussian Inequalities. Orthogonal Expansions. Excursion Probabilities. Stationary Fields -- Parat II. Geometry. Integral Geometry. Differential Geometry. Piecewise Smooth Manifolds. Critical Point Theory. Volume of Tubes -- Part III. The Geometry of Random Fields. Random Fields on Euclidean Spaces. Random Fields on Manifolds. Mean Intrinsic Volumes. Excursion Probabilities for Smooth Fields. Non-Gaussian Geometry -- References -- Index
Summary
A monograph that is devoted to a fresh approach to geometric problems arising in the study of random fields, namely, the geometry of excursion sets of random fields and the related Euler characteristic approach to extremal probabilities
Bibliography
Includes bibliographical references (pages 435-442)-and indexes
