Stochastic Approximation and Its Applications
Title | Stochastic Approximation and Its Applications PDF eBook |
Author | Han-Fu Chen |
Publisher | Springer Science & Business Media |
Pages | 369 |
Release | 2005-12-30 |
Genre | Mathematics |
ISBN | 0306481669 |
Estimating unknown parameters based on observation data conta- ing information about the parameters is ubiquitous in diverse areas of both theory and application. For example, in system identification the unknown system coefficients are estimated on the basis of input-output data of the control system; in adaptive control systems the adaptive control gain should be defined based on observation data in such a way that the gain asymptotically tends to the optimal one; in blind ch- nel identification the channel coefficients are estimated using the output data obtained at the receiver; in signal processing the optimal weighting matrix is estimated on the basis of observations; in pattern classifi- tion the parameters specifying the partition hyperplane are searched by learning, and more examples may be added to this list. All these parameter estimation problems can be transformed to a root-seeking problem for an unknown function. To see this, let - note the observation at time i. e. , the information available about the unknown parameters at time It can be assumed that the parameter under estimation denoted by is a root of some unknown function This is not a restriction, because, for example, may serve as such a function.
Stochastic Approximation and Recursive Algorithms and Applications
Title | Stochastic Approximation and Recursive Algorithms and Applications PDF eBook |
Author | Harold Kushner |
Publisher | Springer Science & Business Media |
Pages | 485 |
Release | 2006-05-04 |
Genre | Mathematics |
ISBN | 038721769X |
This book presents a thorough development of the modern theory of stochastic approximation or recursive stochastic algorithms for both constrained and unconstrained problems. This second edition is a thorough revision, although the main features and structure remain unchanged. It contains many additional applications and results as well as more detailed discussion.
Stochastic Approximation and Its Applications
Title | Stochastic Approximation and Its Applications PDF eBook |
Author | Han-Fu Chen |
Publisher | Springer |
Pages | 0 |
Release | 2010-12-10 |
Genre | Mathematics |
ISBN | 9781441952288 |
Estimating unknown parameters based on observation data conta- ing information about the parameters is ubiquitous in diverse areas of both theory and application. For example, in system identification the unknown system coefficients are estimated on the basis of input-output data of the control system; in adaptive control systems the adaptive control gain should be defined based on observation data in such a way that the gain asymptotically tends to the optimal one; in blind ch- nel identification the channel coefficients are estimated using the output data obtained at the receiver; in signal processing the optimal weighting matrix is estimated on the basis of observations; in pattern classifi- tion the parameters specifying the partition hyperplane are searched by learning, and more examples may be added to this list. All these parameter estimation problems can be transformed to a root-seeking problem for an unknown function. To see this, let - note the observation at time i. e. , the information available about the unknown parameters at time It can be assumed that the parameter under estimation denoted by is a root of some unknown function This is not a restriction, because, for example, may serve as such a function.
Stochastic Approximation and Optimization of Random Systems
Title | Stochastic Approximation and Optimization of Random Systems PDF eBook |
Author | Lennart Ljung |
Publisher | Birkhauser |
Pages | 128 |
Release | 1992 |
Genre | Mathematics |
ISBN | 9780817627331 |
Stochastic approximation and its applications
Title | Stochastic approximation and its applications PDF eBook |
Author | Madanlal T. Wasan |
Publisher | |
Pages | 29 |
Release | 1967 |
Genre | |
ISBN |
Approximation and Weak Convergence Methods for Random Processes, with Applications to Stochastic Systems Theory
Title | Approximation and Weak Convergence Methods for Random Processes, with Applications to Stochastic Systems Theory PDF eBook |
Author | Harold Joseph Kushner |
Publisher | MIT Press |
Pages | 296 |
Release | 1984 |
Genre | Computers |
ISBN | 9780262110907 |
Control and communications engineers, physicists, and probability theorists, among others, will find this book unique. It contains a detailed development of approximation and limit theorems and methods for random processes and applies them to numerous problems of practical importance. In particular, it develops usable and broad conditions and techniques for showing that a sequence of processes converges to a Markov diffusion or jump process. This is useful when the natural physical model is quite complex, in which case a simpler approximation la diffusion process, for example) is usually made. The book simplifies and extends some important older methods and develops some powerful new ones applicable to a wide variety of limit and approximation problems. The theory of weak convergence of probability measures is introduced along with general and usable methods (for example, perturbed test function, martingale, and direct averaging) for proving tightness and weak convergence. Kushner's study begins with a systematic development of the method. It then treats dynamical system models that have state-dependent noise or nonsmooth dynamics. Perturbed Liapunov function methods are developed for stability studies of nonMarkovian problems and for the study of asymptotic distributions of non-Markovian systems. Three chapters are devoted to applications in control and communication theory (for example, phase-locked loops and adoptive filters). Smallnoise problems and an introduction to the theory of large deviations and applications conclude the book. Harold J. Kushner is Professor of Applied Mathematics and Engineering at Brown University and is one of the leading researchers in the area of stochastic processes concerned with analysis and synthesis in control and communications theory. This book is the sixth in The MIT Press Series in Signal Processing, Optimization, and Control, edited by Alan S. Willsky.
Stochastic Approximation
Title | Stochastic Approximation PDF eBook |
Author | Vivek S. Borkar |
Publisher | Springer |
Pages | 177 |
Release | 2009-01-01 |
Genre | Mathematics |
ISBN | 938627938X |