In this post, we will see two volume book titled Topics In The Theory Of Random Noise by R. L. Stratonovich.

# About the books

The present book, in two volumes, is concerned with a variety of topics which have been left to one side, as it were, but which are nevertheless of great practical importance. In particular, we have in mind problems involving the effects of noise on electronic relays and vacuum- tube oscillators. Recently, there has been increased interest in the operation of switching devices and self-excited systems, not only because of the development of methods of coherent radar detection, but also in connection with such problems as increasing the accuracy of time measurements, designing particle accelerators and computing machines, etc. However, the journal literature in these new fields of statistical radio engineering is hard to penetrate. In the present book, noise in relays and oscillators is studied in an organized fashion, from a rather general point of view. Material that can be found in the literature has been systematized, and the results of some original investigations by the author have been included. The physical treatment of the results obtained may be a bit sketchy, but it seems to us that brevity coupled with wide coverage is justified in this instance, since the rapid growth in the total number of published papers has increased the need for some kind of survey, even one resembling a handbook.

Part I of Volume I is devoted to a review of the mathematical results used later in the book. In many places, it has seemed appropriate, for the sake of brevity, to depart from the usual presentation of the basic concepts and results of probability theory. The reader who is not familiar with this necessary background material can refer to any one of a number of textbooks. Those already acquainted with elementary probability theory will find that Part 1 contains a different treatment of certain well-known topics, in addition to some new results. In fact, Part I ought not to be devoid of interest even to mathematicians, provided, of course, that they make due allowances for the heuristic level of rigor adopted.

In Volume I, Part 2 and in Volume II, we systematically use the methods just enumerated to solve specific problems of statistical radio engineering. At the same time, we try to explain the conditions under which the various methods of analyzing noise phenomena are applicable. Perhaps some of the methods are given in more detail than is necessary for immediate applications3but this is done with a view to further development of the tools needed for future work. It is reasonable to expect that the progressively more complicated problems which come up in engineering practice will require the use of progressively more sophisticated methods of analysis. The author will regard his task as accomplished if this book serves in some measure to broaden the theoretical outlook of radio scientists, by helping them master certain methods which they may find novel at first. Although the material given here is intended primarily for specialists in the field of statistical radio engineering, it should also interest scientists working in other fields where similar statistical methods can be profitably used.

The book was translated from Russian by Richard A. Silverman and were published in 1963 and 1967.

Credits to original uploader.

You can get the Volume 1 here and Volume 2 here.

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# Contents

# Volume 1

## Part 1 — GENERAL THEORY OF RANDOM PROCESSES

Chapter 1. Random Functions and Their Statistical Characteristics 3

Chapter 2. Stationary Random Processes and Spectral Densities 21

Chapter 3. Gaussian and Non-Gaussian Random Processes. Quasi-Moment Functions 39

Chapter 4. Markov Processes and Related Processes 55

Chapter 5. Nonstationary Random Processes 131

Chapter 6. Systems of Random Points and Related Random Functions 143

Chapter 7. Narrow-Band Random Processes 177

## Part 2 — NONLINEAR TRANSFORMATIONS OF SIGNALS AND NOISE

Chapter 8. Zero-Memory Nonlinear Transformations 206

Chapter 9. Nonlinear transformations with memory, Detection of Random Signals 245

Bibliography 287

# Volume 2

## Part 1 — PEAKS OF RANDOM FUNCTIONS AND THE EFFECT OF NOISE ON RELAYS

Chapter 1. The Mean Number of Peaks of a Random Function 3

Chapter 2. The Duration of Peaks of a Markov Process 21

Chapter 3. Smoothly Varying Noise and its Effect on Relays 51

## Part 2 — NONLINEAR SELF-EXCITED OSCILLATIONS IN THE PRESENCE OF NOISE

Chapter 4. Basic Equations Describing the Operation of an Oscillator in the Presence of Noise 87

Chapter 5. Methods of Solving the Simplified Equations 120

Chapter 6. Effect of Weak Internal Noise on an Oscillator 147

Chapter 7. Effect of Strong External Noise on an Oscillator 170

Chapter 8. Effect of Slowly Varying Ambient Noise on an Oscillator 193

Chapter 9. Synchronization of an Oscillator in the Presence of Noise 222

Chapter 10. Parametric Oscillations 277

Bibliography 323

Index 327