Stochastic Processes in Engineering Systems

by E. Wong, B. Hajek

Overview

This book is a revision of Shastic Processes in Information and Dynamical Systems written by the first author (E.W.) and published in 1971. The book was originally written, and revised, to provide a graduate level text in shastic processes for students whose primary interest is its applications. It treats both the traditional topic of sta­ tionary processes in linear time-invariant systems as well as the more modern theory of shastic systems in which dynamic structure plays a profound role. Our aim is to provide a high-level, yet readily acces­ sible, treatment of those topics in the theory of continuous-parameter shastic processes that are important in the analysis of information and dynamical systems. The theory of shastic processes can easily become abstract. In dealing with it from an applied point of view, we have found it difficult to decide on the appropriate level of rigor. We intend to provide just enough mathematical machinery so that important results can be stated PREFACE vi with precision and clarity; so much of the theory of shastic processes is inherently simple if the suitable framework is provided. The price of providing this framework seems worth paying even though the ul­ timate goal is in applications and not the mathematics per se.

Product Details

ISBN-13:	9781461295457
Publisher:	Springer New York
Publication date:	09/30/2011
Series:	Springer Texts in Electrical Engineering
Edition description:	Second Edition 1985
Pages:	361
Product dimensions:	6.10(w) x 9.25(h) x 0.03(d)

Table of Contents

1 Elements of Probability Theory.- 1. Events and probability.- 2. Measures on finite-dimensional spaces.- 3. Measurable functions and random variables.- 4. Sequences of events and random variables.- 5. Expectation of random variables.- 6. Convergence concepts.- 7. Independence and conditional expectation.- 2 Shastic Processes.- 1. Definition and preliminary considerations.- 2. Separability and measurability.- 3. Gaussian processes and Brownian motion.- 4. Continuity.- 5. Markov processes.- 6. Stationarity and ergodicity.- 3 Second-Order Processes.- 1. Introduction.- 2. Second-order continuity.- 3. Linear operations and second-order calculus.- 4. Orthogonal expansions.- 5. Wide-sense stationary processes.- 6. Spectral representation.- 7. Lowpass and bandpass processes.- 8. White noise and white-noise integrals.- 9. Linear prediction and filtering.- 4 Shastic Integrals and Shastic Differential Equations.- 1. Introduction.- 2. Shastic integrals.- 3. Processes defined by shastic integrals.- 4. Shastic differential equations.- 5. White noise and shastic calculus.- 6. Generalizations of the shastic integral.- 7. Diffusion equations.- 5 One-Dimensional Diffusions.- 1. Introduction.- 2. The Markov semigroup.- 3. Strong Markov processes.- 4. Characteristic operators.- 5. Diffusion processes.- 6 Martingale Calculus.- 1. Martingales.- 2. Sample-path integrals.- 3. Predictable processes.- 4. Isometric integrals.- 5. Semimartingale integrals.- 6. Quadratic variation and the change of variable formula.- 7. Semimartingale exponentials and applications.- 7 Detection and Filtering.- 1. Introduction.- 2. Likelihood ratio representation.- 3. Filter representation—change of measure derivation.- 4. Filter representation—innovations derivation.- 5. Recursiveestimation.- 8 Random Fields.- 1. Introduction.- 2. Homogenous random fields.- 3. Spherical harmonics and isotropic random fields.- 4. Markovian random fields.- 5. Multiparameter martingales.- 6. Shastic differential forms.- References.- Solutions to Exercises.