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The detailed solution to all the exercises and practical work are given together at the end of the book in ssss1.
1
Elementary Probabilities and an Introduction to Stochastic Processes
This chapter reviews the basic concepts related to probability and random variables which will be useful for the rest of this text. For a more detailed explanation as well as demonstrations, the readers may refer to [BAR 07, DAC 82, FOA 03, OUV 08, OUV 09] in French and [BIL 12, CHU 01, DUR 10, KAL 02, SHI 00] in English. The readers who are already familiar with these concepts may proceed straight to ssss1, which introduces the concept of stochastic processes.
This chapter begins with a brief summary of the concepts of a σ-algebra in ssss1. These concepts will help in understanding the construction of the properties of conditional expectation in ssss1. We then study the chief definitions and properties of random variables and their distribution in ssss1. There is an emphasis on discrete random variables as this entire book essentially studies discrete cases. ssss1 defines a stochastic process, which is the main subject studied in this book. Finally, there are exercises in handling these different concepts in ssss1. The solutions are given in ssss1.