Non-Linear Transformations of Stochastic Processes
- 1st Edition - May 12, 2014
- Imprint: Pergamon
- Editors: P. I. Kuznetsov, R. L. Stratonovich, V. I. Tikhonov
- Language: English
- eBook ISBN:9 7 8 - 1 - 4 8 3 2 - 8 2 6 8 - 8
Non-Linear Transformations of Stochastic Processes focuses on the approaches, methodologies, transformations, and computations involved in the non-linear transformations of… Read more
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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.
Foreword to English Edition
Authors' Foreword
Chapter 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 Pulses
Chapter 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 Finder
Chapter 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 Systems
Chapter 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 Excursions
Chapter 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 Functions
Index
- Edition: 1
- Published: May 12, 2014
- Imprint: Pergamon
- Language: English
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