This book is based on the lecture notes that I have been using since 1988
for the course entitled Processus stochastiques at the Ecole Polytechnique de
Montreal. This course is mostly taken by students in electrical engineering
and applied mathematics, notably in operations research, who are generally
at the master's degree level. Therefore, we take for granted that the reader
is familiar with elementary probability theory. However, in order to write a
self-contained book, the first chapter of the text presents the basic results in
probability.
This book aims at providing the readers with a reference that covers the
most important subjects in the field of stochastic processes and that is
accessible to students who don't necessarily have a sound theoretical knowledge
of mathematics. Indeed, we don't insist very much in this volume on
rigorous proofs of the theoretical results; rather, we spend much more time on
applications of these results.
After the review of elementary probability theory in Chapter 1, the
remainder of this chapter is devoted to random variables and vectors. In particular,
we cover the notion of conditional expectation, which is very useful in the
sequel.