Large Deviation Techniques in Decision, Simulation, and Estimation
Wiley, 15 août 1990 - 270 pages
Random 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.
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Cramers Theorem and Extensions
Sanovs Theorem and the Contraction Principle
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Analysis appendix approaches infinity approaches zero bounded continuous function chapter closed sets compute constant continuous function continuous-time convergence in distribution convex function covariance Cramer's theorem defined denote derivative detector differential equation eigenfunctions eigenvalue eigenvector empirical distributions Euler's equation example exercise exists exponential finite state space Gartner-Ellis theorem given Hence iid sequence implies integral interval large deviation principle large deviation theory large numbers largest eigenvalue lemma Let us consider lim e log limit lower bound Markov chain Markov processes matrix mean value memoryless minimizing nonlinearity Note obtain open set operator optimal optimum parameter perturbation probability distribution probability measures probability of error Prohorov metric proof queue rate function Sanov's theorem sequence of random solution sourceword space of probability stationary distribution Statistical stochastic stochastic differential equation subset Suppose Toeplitz trajectory transition probabilities twisted distribution type II error upper bound variance zero mean