Large Deviation Techniques in Decision, Simulation, and EstimationRandom Data Analysis and Measurement Procedures Second Edition Julius S. Bendat and Allan G. Piersol The latest techniques for analysis and measurement of stationary and nonstationary random data passing through physical systems are described in this extensive revision and update. It includes new modern data processing procedures and new statistical error analysis formulas for the evaluation of estimates in single input/output and multiple input/output problems, plus new material on Hilbert transforms, multiple array models, and more. Chapters on statistical errors in basic and advanced estimates represent the most complete derivation and summary of these matters in print. 1986 (0 471-04000-2) 566 pp. Linear Stochastic Systems Peter E. Caines This outstanding text provides a unified and mathematically rigorous exposition of linear stochastic system theory The comprehensive format includes a full treatment of the fundamentals of stochastic processes and the construction of stochastic systems. It then presents an integrated view of the interrelated theories of prediction, realization (or modeling), parameter estimation and control. It also features in-depth coverage of system identification, with chapters on maximum likelihood estimation for Gaussian ARMAX and state space systems, minimum prediction error identification methods, nonstationary system identification, linear-quadratic stochastic control and concludes with a discussion of stochastic adaptive control. 1988 (0 471-08101-9) 874 pp. Introduction to the theory of Coverage Processes Peter Hall Coverage processes are finding increasing application in such diverse areas as queueing theory, ballistics, and physical chemistry. Drawing on methodology from several areas of probability theory and mathematics, this monograph provides a succinct and rigorous development of the mathematical theory of models for random coverage patterns. 1988 (0 471-85702-5) 408 pp. |
Contents
Introduction | 1 |
Cramérs Theorem and Extensions | 7 |
Sanovs Theorem and the Contraction Principle | 25 |
Copyright | |
18 other sections not shown
Common terms and phrases
asymptotic bounded continuous function chapter closed set compute consider continuous function convergence in distribution covariance defined denote density derivative detector eigenfunctions eigenvalue eigenvector empirical distributions estimate Euler's equation exercise exponential finite state space Gaussian random given H₁ Hence hypothesis implies inequality integral interval large deviation principle large deviation theory largest eigenvalue lemma lim log limit log M(0 log p(x lower bound Markov chain Markov processes matrix mean value memoryless moment generating function nonlinearity Note open set operator optimal optimum p(xy P₁ perturbation probability distribution probability measures probability of error problem proof queue random process random variables rate function S₁ samples Sanov's theorem simulation solution Statistical stochastic subset Suppose Toeplitz Toeplitz matrix trajectory transition probabilities twisted type II error upper bound variance vector x₁ y₁