Theory and Simulation of Random Phenomena: Mathematical Foundations and Physical Applications

This book provides a comprehensive understanding of probability theory and stochastic processes, equipping readers with the skills to develop algorithms that simulate realistic physical systems. It is ideal for graduate students and has connections with various fields of pure and applied physics.

Format: Hardback
Length: 235 pages
Publication date: 22 June 2018
Publisher: Springer International Publishing AG

The purpose of this book is multifaceted: firstly, it seeks to provide the reader with a comprehensive grasp of the fundamental principles of probability theory and stochastic processes, offering a step-by-step journey from basic probability theory to advanced topics, such as stochastic differential equations, often encountered in textbooks that demand a solid mathematical foundation. Secondly, while guiding the reader on this intellectual expedition, it endeavors to impart the knowledge required to develop algorithms capable of simulating realistic physical systems. Connections with various branches of pure and applied physics, ranging from quantum mechanics to econophysics, are elucidated. Furthermore, the inclusion of fully solved exercises empowers the reader to acquire knowledge rapidly and to delve into topics not covered in the main text. This book will particularly appeal to graduate students eager to learn how to simulate physical systems and to delve deeper into the mathematical framework, which has profound connections with modern quantum field theory.

Probability theory and stochastic processes form the cornerstone of this comprehensive book, designed to equip readers with a deep understanding of their foundations.

It begins with a gentle introduction to basic probability theory, guiding the reader through concepts such as random variables, probability distributions, and conditional probability. As the journey progresses, the book delves into more advanced topics, including Markov chains, stochastic differential equations, and Brownian motion. Each chapter is accompanied by detailed explanations, examples, and exercises, allowing readers to apply their knowledge and reinforce their understanding.

What sets this book apart is its emphasis on developing algorithms that simulate realistic physical systems. The author draws connections between probability theory and various fields of pure and applied physics, providing a holistic perspective on the subject.

For graduate students seeking to enhance their knowledge of simulation and deepen their understanding of the mathematical framework, this book is an invaluable resource. It offers a comprehensive treatment of probability theory and stochastic processes, equipping readers with the tools they need to tackle complex problems and contribute to the field.

With its clear and concise writing style, extensive illustrations, and comprehensive coverage, this book is suitable for both undergraduate students and professionals in the fields of mathematics, physics, and engineering.

Weight: 510g
Dimension: 239 x 176 x 19 (mm)
ISBN-13: 9783319905143
Edition number: 1st ed. 2018