Non-Linear Transformations of Stochastic Processes
Published on 12. May 2014
514 pages
978-1-4832-8268-8 (ISBN)
Description
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.
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Content
Foreword to English EditionAuthors' ForewordChapter I Some Problems of the Theory of Stochastic Processes 1 The Transmission of Certain Random Functions Through Linear Systems 2 The Transmission of Random Functions Through Non-Linear Systems 3 Quasi-Moment Functions in the Theory of Random Processes 4 The Effect of Non-Normal Fluctuations on Linear Systems 5 Correlation Functions in the Theory of Brownian Motion Generalization of the Fokker-Planck Equation 6 A Note on the Mathematical Theory of Correlated Random Points 7 The Correlation Functions of Random Sequences of Rectangular PulsesChapter II The Effect of Noise on Certain Non-Linear Elements 8 A Method of Determining the Envelope of Quasi-Harmonic Fluctuations 9 The Effect of Electrical Fluctuations on a Detector (Envelope Method) 10 The Effect of Fluctuations on a Detector and Filter 11 A Note on the Problem of Measuring Electrical Fluctuations with the Aid of Thermoelectric Devices 12 The Response of Typical Non-Linear Elements to Normally Fluctuating Inputs 13 The Effect of Signal and Noise on Non-Linear Elements (The Direct Method) 14 Approximate Method of Calculating the Correlation Function of Stochastic Signals 15 The Effect of Fluctuations on the Operation of an Automatic Range FinderChapter III The Effect of Fluctuations on Oscillator Operation 16 The Effect of Electrical Fluctuations on a Valve Oscillator 17 The Effect of Small Fluctuations on Oscillator Operation 18 The Fluctuating Nature of the Establishment of Oscillation Amplitude in an Oscillator 19 The Effect of Slow Fluctuations on an Oscillator 20 The Effect of Noise on an Oscillator with Fixed Excitation 21 Oscillator Synchronization in the Presence of Noise 22 Establishment of the Synchronous Phase in a Self-Oscillatory Circuit in the Presence of Noise 23 Establishment of Amplitude in a Synchronized Oscillator in the Presence of Fluctuation Noise 24 The Effect of noise on the Operation of a Phase AFC Circuit 25 Operation of a Phase AFC Circuit in the Presence of Noise 26 Parametric Effect of a Random Force on Linear and Non-Linear Oscillatory Systems 27 The Simultaneous Parametric Effect of a Harmonic and Random Force on Oscillatory SystemsChapter IV Random Function Excursions 28 On the Duration of Excursions of Random Functions 29 The Distribution of the Duration of Excursions of Normal Fluctuations 30 An Experimental Study of the Length Distribution Law of Fluctuation Excursions 31 Fluctuation Excursions and their Correlation 32 Probability Densities for the Duration of Fluctuation Excursions 33 The Effect of Differentiating and Integrating on the Average Number of ExcursionsChapter V Optimum Filtration 34 The Conditional Distribution of Correlated Random Points and the use of Correlation for Optimum Nitration of a Pulse Signal from Noise 35 A Contribution to the Theory of the Optimum Non-Linear Filtration of Random Functions 36 Conditional Markov Processes 37 Optimum Non-Linear Systems for Isolating a Signal with Constant Parameters from Noise 38 Application of the Theory of Markov Processes to the Optimum Nitration of Signals 39 Some Problems in Conditional Probability and Quasi-Moment FunctionsIndex
