Large Deviation Techniques in Decision, Simulation, and Estimation
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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Cramérs Theorem and Extensions
Sanovs Theorem and the Contraction Principle
11 other sections not shown
Analysis Applications approaches approximation arguments associated assume asymptotic bound called chapter choose closed compute condition consider constant continuous convergence convex defined definition denote density depend derivative differentiable distribution eigenvalue eigenvector equal equation error estimate example exercise exists exponential expression finite fixed Gaussian given gives Hence hypothesis implies important independent integral interest interval large deviation large deviation principle limit lower bound Markov chain matrix mean mean value method minimizing Note observations obtain open set operator optimal performance perturbation positive probability probability measures problem proof random variables rate function respect samples Second sequence simple simulation solution space Statistical stochastic differential equation Suppose term theorem theory trajectory transition true twisted usually variance vector zero