Preface For about ten years between 1973 and 1986 the author was delivering a one- year topics course "Random Processes" at the Department of Mechanics and Mathematics of Moscow State University. This topics course was obligatory for third-fourth year undergraduate students (about 20 years of age) with major in probability theory and its applications. With great sympathy I remember my first students in this course: M. Safonov, A. Veretennikov, S. Anulova, and L. Mikhailovskaya. During these years the contents of the course gradually evolved, simplifying and shortening to the shape which has been presented in two 83 and 73 page long rotaprint lecture notes published by Moscow State University in 1986 and 1987. In 1990 I emigrated to the USA and in 1998 got the opportunity to present parts of the same course as a one-quarter topics course in probability theory for graduate students at the University of Minnesota. I thus had the opportunity to test the course in the USA as well as on several generations of students in Russia. What the reader finds below is a somewhat extended version of my lectures and the recitations which went along with the lectures in Russia. The theory of random processes is an extremely vast branch of math- ematics which cannot be covered even in ten one-year topics courses with minimal intersection of contents. Therefore, the intent of this book is to get the reader acquainted only with some parts of the theory. The choice of these parts was mainly defined by the duration of the course and the au- thor's taste and interests. However, there is no doubt that the ideas, facts, and techniques presented here will be useful if the reader decides to move on and study some other parts of the theory of random processes. From the table of contents the reader can see that the main topics of the book are the Wiener process, stationary processes, infinitely divisible XI
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