Non-Linear Transformations of Stochastic Processes

Non-Linear Transformations of Stochastic Processes
Author: P. I. Kuznetsov
Publisher: Elsevier
Total Pages: 515
Release: 2014-05-12
Genre: Mathematics
ISBN: 1483282686

Non-Linear Transformations of Stochastic Processes focuses on the approaches, methodologies, transformations, and computations involved in the non-linear transformations of stochastic processes. The selection first underscores some problems of the theory of stochastic processes and the transmission of random functions through non-linear systems. Discussions focus on the transformation of moment functions for the general non-linear transformation; conversion formulas for correlation functions; transformation of moment functions for the simplest type of non-linear transformation; and normalization of the linear system of probability distribution laws. The text then ponders on quasi-moment functions in the theory of random processes and correlation functions in the theory of the Brownian motion generalization of the Fokker-Planck equation. The manuscript elaborates on the correlation functions of random sequences of rectangular pulses; method of determining the envelope of quasi-harmonic fluctuations; and the problem of measuring electrical fluctuations with the aid of thermoelectric devices. The book then examines the effect of signal and noise on non-linear elements and the approximate method of calculating the correlation function of stochastic signals. The selection is a dependable source of information for researchers interested in the non-linear transformations of stochastic processes.

Topics In the Theory of Random Noise

Topics In the Theory of Random Noise
Author: R.L. Stratonovich
Publisher: CRC Press
Total Pages: 348
Release: 1967-01-01
Genre: Mathematics
ISBN: 9780677007908

In two main sections, this volume covers peaks of random functions and the effects of noise on relays and nonlinear self-excited oscillations in the presence of noise. Includes bibliographic references and index.

Statistics of Random Processes

Statistics of Random Processes
Author: Robert Liptser
Publisher: Springer Science & Business Media
Total Pages: 450
Release: 2001
Genre: Mathematics
ISBN: 9783540639299

These volumes cover non-linear filtering (prediction and smoothing) theory and its applications to the problem of optimal estimation, control with incomplete data, information theory, and sequential testing of hypothesis. Also presented is the theory of martingales, of interest to those who deal with problems in financial mathematics. These editions include new material, expanded chapters, and comments on recent progress in the field.

Analysis and Simulation of Noise in Nonlinear Electronic Circuits and Systems

Analysis and Simulation of Noise in Nonlinear Electronic Circuits and Systems
Author: Alper Demir
Publisher: Springer Science & Business Media
Total Pages: 278
Release: 2012-12-06
Genre: Technology & Engineering
ISBN: 1461560632

In electronic circuit and system design, the word noise is used to refer to any undesired excitation on the system. In other contexts, noise is also used to refer to signals or excitations which exhibit chaotic or random behavior. The source of noise can be either internal or external to the system. For instance, the thermal and shot noise generated within integrated circuit devices are in ternal noise sources, and the noise picked up from the environment through electromagnetic interference is an external one. Electromagnetic interference can also occur between different components of the same system. In integrated circuits (Ies), signals in one part of the system can propagate to the other parts of the same system through electromagnetic coupling, power supply lines and the Ie substrate. For instance, in a mixed-signal Ie, the switching activity in the digital parts of the circuit can adversely affect the performance of the analog section of the circuit by traveling through the power supply lines and the substrate. Prediction of the effect of these noise sources on the performance of an electronic system is called noise analysis or noise simulation. A methodology for the noise analysis or simulation of an electronic system usually has the following four components: 2 NOISE IN NONLINEAR ELECTRONIC CIRCUITS • Mathematical representations or models for the noise sources. • Mathematical model or representation for the system that is under the in fluence of the noise sources.

Stochastic Methods and their Applications to Communications

Stochastic Methods and their Applications to Communications
Author: Serguei Primak
Publisher: John Wiley & Sons
Total Pages: 446
Release: 2005-01-28
Genre: Technology & Engineering
ISBN: 0470021179

Stochastic Methods & their Applications to Communications presents a valuable approach to the modelling, synthesis and numerical simulation of random processes with applications in communications and related fields. The authors provide a detailed account of random processes from an engineering point of view and illustrate the concepts with examples taken from the communications area. The discussions mainly focus on the analysis and synthesis of Markov models of random processes as applied to modelling such phenomena as interference and fading in communications. Encompassing both theory and practice, this original text provides a unified approach to the analysis and generation of continuous, impulsive and mixed random processes based on the Fokker-Planck equation for Markov processes. Presents the cumulated analysis of Markov processes Offers a SDE (Stochastic Differential Equations) approach to the generation of random processes with specified characteristics Includes the modelling of communication channels and interfer ences using SDE Features new results and techniques for the of solution of the generalized Fokker-Planck equation Essential reading for researchers, engineers, and graduate and upper year undergraduate students in the field of communications, signal processing, control, physics and other areas of science, this reference will have wide ranging appeal.

Modern Nonlinear Equations

Modern Nonlinear Equations
Author: Thomas L. Saaty
Publisher: Courier Corporation
Total Pages: 500
Release: 2012-04-26
Genre: Mathematics
ISBN: 0486143767

Covers major types of classical equations: operator, functional, difference, integro-differential, and more. Suitable for graduate students as well as scientists, technologists, and mathematicians. "A welcome contribution." — Math Reviews. 1964 edition.

Non Linear Mathematics Vol. II

Non Linear Mathematics Vol. II
Author: Thomas L. Saaty
Publisher: RWS Publications
Total Pages: 490
Release: 2014-12-22
Genre: Business & Economics
ISBN: 1888603399

Nonlinear equations have existed for hundreds of years; their systematic study, however, is a relatively recent phenomenon. This volume, together with its companion', Nonlinear Matliematics Vol. I, provides exceptionally comprehensive coverage of this recently formed area of study. It encompasses both older and more recent developments in the field of equations, with particular emphasis on nonlinear equations because, as Professor Saaty maintains, "that is what is needed today." Together the two volumes cover all the major types of classical equations (except partial differential equations, which require a separate volume). This volume includes material on seven types: operator equations, functional equations, difference equations, delay-differential equations, integral equations, integro-differential equations and stochastic differential equations. Special emphasis is placed on linear and nonlinear equations in function spaces and On general methods of solving different types of such equations. Above all, this book is practical. It reviews the variety of existing types of equations and provides methods for their solution. It is meant to help the reader acquire new methods for formulating problems. Its clear organization and copious references make it suitable for graduate students as well as scientists, technologists and mathematicians.

Nonlinear Random Vibration

Nonlinear Random Vibration
Author: Cho W.S. To
Publisher: CRC Press
Total Pages: 257
Release: 2000-01-01
Genre: Technology & Engineering
ISBN: 1482287269

This is a systematic presentation of several classes of analytical techniques in non-linear random vibration. The book also includes a concise treatment of Markovian and non-Markovian solutions of non-linear differential equations.