Three coherent parts form the material covered in this text portions of which have not been
widely covered in traditional textbooks. In this coverage the reader is quickly introduced to
several different topics enriched with 175 exercises which focus on real-world problems.
Exercises range from the classics of probability theory to more exotic research-oriented
problems based on numerical simulations. Intended for graduate students in mathematics and
applied sciences the text provides the tools and training needed to write and use programs for
research purposes. The first part of the text begins with a brief review of measure theory and
revisits the main concepts of probability theory from random variables to the standard limit
theorems. The second part covers traditional material on stochastic processes including
martingales discrete-time Markov chains Poisson processes and continuous-time Markov chains.
The theory developed is illustrated by a variety of examples surrounding applications such as
the gambler's ruin chain branching processes symmetric random walks and queueing systems.
The third more research-oriented part of the text discusses special stochastic processes of
interest in physics biology and sociology. Additional emphasis is placed on minimal models
that have been used historically to develop new mathematical techniques in the field of
stochastic processes: the logistic growth process the Wright -Fisher model Kingman's
coalescent percolation models the contact process and the voter model. Further treatment of
the material explains how these special processes are connected to each other from a modeling
perspective as well as their simulation capabilities in C and Matlab(TM).
