LEADER 05481nam 2200781Ia 450 001 9910826818803321 005 20200520144314.0 010 $a9786612687235 010 $a9781282687233 010 $a1282687239 010 $a9780470434642 010 $a0470434643 010 $a9780470434635 010 $a0470434635 035 $a(CKB)1000000000719507 035 $a(EBL)427668 035 $a(OCoLC)476269828 035 $a(SSID)ssj0000191624 035 $a(PQKBManifestationID)11171265 035 $a(PQKBTitleCode)TC0000191624 035 $a(PQKBWorkID)10183740 035 $a(PQKB)10918440 035 $a(MiAaPQ)EBC427668 035 $a(Au-PeEL)EBL427668 035 $a(CaPaEBR)ebr10296500 035 $a(CaONFJC)MIL268723 035 $a(OCoLC)237018337 035 $a(FINmELB)ELB178301 035 $a(Perlego)2770805 035 $a(EXLCZ)991000000000719507 100 $a20080726d2009 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aLevel sets and extrema of random processes and fields /$fJean-Marc Azais, Mario Wschebor 205 $a1st ed. 210 $aHoboken, N.J. $cWiley$dc2009 215 $a1 online resource (407 p.) 300 $aDescription based upon print version of record. 311 08$a9780470409336 311 08$a0470409339 320 $aIncludes bibliographical references and index. 327 $aLEVEL SETS AND EXTREMA OF RANDOM PROCESSES AND FIELDS; CONTENTS; PREFACE; INTRODUCTION; 1 CLASSICAL RESULTS ON THE REGULARITY OF PATHS; 1.1 Kolmogorov's Extension Theorem; 1.2 Reminder on the Normal Distribution; 1.3 0-1 Law for Gaussian Processes; 1.4 Regularity of Paths; Exercises; 2 BASIC INEQUALITIES FOR GAUSSIAN PROCESSES; 2.1 Slepian Inequalities; 2.2 Ehrhard's Inequality; 2.3 Gaussian Isoperimetric Inequality; 2.4 Inequalities for the Tails of the Distribution of the Supremum; 2.5 Dudley's Inequality; Exercises; 3 CROSSINGS AND RICE FORMULAS FOR ONE-DIMENSIONAL PARAMETER PROCESSES 327 $a3.1 Rice Formulas3.2 Variants and Examples; Exercises; 4 SOME STATISTICAL APPLICATIONS; 4.1 Elementary Bounds for P{M >u}; 4.2 More Detailed Computation of the First Two Moments; 4.3 Maximum of the Absolute Value; 4.4 Application to Quantitative Gene Detection; 4.5 Mixtures of Gaussian Distributions; Exercises; 5 THE RICE SERIES; 5.1 The Rice Series; 5.2 Computation of Moments; 5.3 Numerical Aspects of the Rice Series; 5.4 Processes with Continuous Paths; 6 RICE FORMULAS FOR RANDOM FIELDS; 6.1 Random Fields from R(d) to R(d); 6.2 Random Fields from R(d) to R(d ?), d > d ?; Exercises 327 $a7 REGULARITY OF THE DISTRIBUTION OF THE MAXIMUM7.1 Implicit Formula for the Density of the Maximum; 7.2 One-Parameter Processes; 7.3 Continuity of the Density of the Maximum of Random Fields; Exercises; 8 THE TAIL OF THE DISTRIBUTION OF THE MAXIMUM; 8.1 One-Dimensional Parameter: Asymptotic Behavior of the Derivatives of F(M); 8.2 An Application to Unbounded Processes; 8.3 A General Bound for p(M); 8.4 Computing (x) for Stationary Isotropic Gaussian Fields; 8.5 Asymptotics as x +; 8.6 Examples; Exercises; 9 THE RECORD METHOD; 9.1 Smooth Processes with One-Dimensional Parameters 327 $a9.2 Nonsmooth Gaussian Processes9.3 Two-Parameter Gaussian Processes; Exercises; 10 ASYMPTOTIC METHODS FOR AN INFINITE TIME HORIZON; 10.1 Poisson Character of High Up-Crossings; 10.2 Central Limit Theorem for Nonlinear Functionals; Exercises; 11 GEOMETRIC CHARACTERISTICS OF RANDOM SEA WAVES; 11.1 Gaussian Model for an Infinitely Deep Sea; 11.2 Some Geometric Characteristics of Waves; 11.3 Level Curves, Crests, and Velocities for Space Waves; 11.4 Real Data; 11.5 Generalizations of the Gaussian Model; Exercises; 12 SYSTEMS OF RANDOM EQUATIONS; 12.1 The Shub-Smale Model 327 $a12.2 More General Models12.3 Noncentered Systems (Smoothed Analysis); 12.4 Systems Having a Law Invariant Under Orthogonal Transformations and Translations; 13 RANDOM FIELDS AND CONDITION NUMBERS OF RANDOM MATRICES; 13.1 Condition Numbers of Non-Gaussian Matrices; 13.2 Condition Numbers of Centered Gaussian Matrices; 13.3 Noncentered Gaussian Matrices; REFERENCES AND SUGGESTED READING; NOTATION; INDEX 330 $aA timely and comprehensive treatment of random field theory with applications across diverse areas of study 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 mo 606 $aGaussian processes 606 $aLevel set methods 606 $aRandom fields 606 $aStochastic processes 615 0$aGaussian processes. 615 0$aLevel set methods. 615 0$aRandom fields. 615 0$aStochastic processes. 676 $a519.2/3 700 $aAzais$b Jean-Marc$f1957-$01615068 701 $aWschebor$b Mario$055247 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910826818803321 996 $aLevel sets and extrema of random processes and fields$93945132 997 $aUNINA