The purpose of this book is twofold: first it sets out to equip the reader with a sound
understanding of the foundations of probability theory and stochastic processes offering
step-by-step guidance from basic probability theory to advanced topics such as stochastic
differential equations which typically are presented in textbooks that require a very strong
mathematical background. Second while leading the reader on this journey it aims to impart
the knowledge needed in order to develop algorithms that simulate realistic physical systems.
Connections with several fields of pure and applied physics from quantum mechanics to
econophysics are provided. Furthermore the inclusion of fully solved exercises will enable
the reader to learn quickly and to explore topics not covered in the main text. The book will
appeal especially to graduate students wishing to learn how to simulate physical systems and to
deepen their knowledge of the mathematical framework which has very deep connections with
modern quantum field theory.
