LEVEL SETS AND EXTREMA OF RANDOM PROCESSES AND FIELDS; CONTENTS; PREFACE; INTRODUCTION; 1 CLASSICAL RESULTS ON THE REGULARITY OF PATHS; 2 BASIC INEQUALITIES FOR GAUSSIAN PROCESSES; 3 CROSSINGS AND RICE FORMULAS FOR ONE-DIMENSIONAL PARAMETER PROCESSES; 4 SOME STATISTICAL APPLICATIONS; 5 THE RICE SERIES; 6 RICE FORMULAS FOR RANDOM FIELDS; 7 REGULARITY OF THE DISTRIBUTION OF THE MAXIMUM; 8 THE TAIL OF THE DISTRIBUTION OF THE MAXIMUM; 9 THE RECORD METHOD; 10 ASYMPTOTIC METHODS FOR AN INFINITE TIME HORIZON; 11 GEOMETRIC CHARACTERISTICS OF RANDOM SEA WAVES; 12 SYSTEMS OF RANDOM EQUATIONS
Summary
Level Sets and Extrema of Random Processes and Fields discusses how to understand the properties of the level sets of paths as well as how to compute the probability distribution of its extremal values, which are two general classes of problems that arise in the study of random processes and fields and in related applications. This book provides a unified and accessible approach to these two topics and their relationship to classical theory and Gaussian processes and fields, and the most modern research findings are also discussed. The authors begin with an introduction to the basic concepts o
Bibliography
Includes bibliographical references (pages 373-388) and index
