Engineering applications of stochastic processes: Theory, problems and solutions: Alexander Zayezdny, Daniel Tabak and Dov Wulich
✍ Scribed by J. Michálek
- Publisher
- Elsevier Science
- Year
- 1991
- Tongue
- English
- Weight
- 126 KB
- Volume
- 27
- Category
- Article
- ISSN
- 0005-1098
No coin nor oath required. For personal study only.
✦ Synopsis
THIS BOOK was published in the series Applied and Engineering Mathematics and is dedicated to specialists in engineering-oriented disciplines. As is said in the foreword, the main purpose is to give a systematic presentation of the theoretical and practical basic notions of probabilistic calculus and to show close connections with disciplines, such as electronic communication, radar and automatic control. The book is intended for undergraduate and graduate students and practical engineers specializing in the areas mentioned above. It might be used as a self-study text or a text-book for courses on applications of random processes in technical areas.
The authors chose a very difficult task to write a book suitable both for practice and for students, in a field as large as utilization of probability theory and stochastic processes in engineering applications. With respect to this fact it is necessary to mention the contents of the book to show which parts of the theory of probability and random processes were chosen by the authors as most important from the view of practice.
The book is subdivided into two parts: Random Variables and Random Processes. The first part presents chapters dedicated to the probability theory; the other touches the most important cases of random processes which can be met in practice.
Chapter 1 introduces the basic concepts and definitions of probability, the basic rules of calculating with probabilities and the conditional probability and the Bayes formula. The notion of mutually independent trials and the de Moivre-Laplace theorem are explained in Chapter 2. Chapter 3 deals with the notion of a random variable and its probability distribution function. The characteristic function is also introduced. The notion of entropy, very important in statistical communication methods, is discussed too. Chapter 4 gives a solution of a very important problem, related to nonlinear networks, finding the probability distribution of the function of a random variable. This topic is continued in Chapter 11. Chapter 5 is devoted to the multidimensional-vector---case of random variables with a special emphasis on the two-dimensional case. Chapter 6 deals with probability theory, and introduces the laws of large numbers.
Chapters 7-11 form the second part of the book, which is devoted to random processes. The notion of a random process, correlation and spectral analysis are presented in Chapter 7. Chapters 8 and 9 are devoted to the canonical representation of random variables and random processes. Chapter 10 deals with linear systems and their responses to random inputs. The classical case with a time-invariant system and a weakly stationary input is considered. Chapter 11 is the largest chapter and discusses some nonlinear systems and their behaviour under random inputs. Two examples are presented: the inertia-less system and the inertial one--the main topic of this chapter. A variety of methods for overcoming troubles with the nonlinear character of such systems are discussed in detail. An Appendix offers special tables of probability distributions and their numerical characteristics.