This book is a final year undergraduate text on stochastic processes. It consists of seven chapters. The first chapter contains a brief introduction to probability, including conditional probability and independence. Conditional expectation is treated in detail in the second chapter as a crucial tool of stochastic processes. The authors begin with conditioning on an event and culminate with the general definition of conditional expectation and its properties. Chapter 3 is devoted to martingales in discrete time. It contains an optional stopping theorem as a main result and a lot of examples. Chapter 4 continues with martingales by presenting Doob’s inequalities and convergence results. Chapter 5 describes time-homogeneous Markov chains, especially their long-time behaviour. Markov chains with a finite state space are treated in full detail. Stochastic processes in continuous time are presented in Chapter 6. Only a few of general notions are given and the authors concentrate on Poisson processes and Brownian motions. Chapter 7 contains the notion and the properties of Itô stochastic integral, Itô formula and the basic notations for stochastic differential equations.
The book contains numerous exercises which form an integral part of the course. Complete solutions are provided at the end of each chapter. Any mathematician having some preliminary level of knowledge can study the book himself. Also, the book is useful for lecturers to involve the students as active participants in the course.