Markov Chains: Gibbs Fields, Monte Carlo Simulation and Queues

This book provides an introduction to stochastic processes for undergraduate and beginning graduate students, with examples from a wide range of domains. It is motivated by significant applications and gradually brings the student to the borders of contemporary research.

Format: Paperback / softback
Length: 557 pages
Publication date: 24 May 2021
Publisher: Springer Nature Switzerland AG

This book serves as an introductory guide to the theory of stochastic processes, particularly suited for undergraduate or beginning graduate students. Its primary objective is to initiate students in the art of stochastic modeling, while also providing insights into significant applications that push the boundaries of contemporary research. The examples presented throughout the book are drawn from a diverse range of domains, including operations research and electrical engineering. Researchers and students in these fields, as well as in physics, biology, and the social sciences, will find this book to be a valuable resource.

The theory of stochastic processes plays a fundamental role in understanding the behavior of systems that are influenced by randomness. It encompasses a wide range of topics, including probability theory, statistics, and mathematical finance, and is applied in various fields such as engineering, economics, and natural sciences. In this book, we will provide a comprehensive introduction to the theory of stochastic processes, covering key concepts, models, and applications.

Probability theory is the foundation of stochastic processes, and we will begin by discussing the basic principles of probability, including random variables, probability distributions, and conditional probability. We will then explore the concept of stochastic processes, which are defined as a collection of random variables that evolve over time according to a set of stochastic differential equations.

One of the key features of stochastic processes is that they can be used to model a wide range of real-world phenomena. For example, stock market prices, weather patterns, and the spread of diseases are all examples of stochastic processes. We will discuss various models that are used to describe these phenomena, including the Black-Scholes model for option pricing, the Markov chain model for discrete-time processes, and the Poisson process for counting events.

In addition to modeling real-world phenomena, stochastic processes are also used in various applications such as risk management, insurance, and finance. We will explore these applications in detail, including the use of stochastic volatility models for pricing options, the Monte Carlo method for simulating financial markets, and the Black-Scholes-Merton model for option valuation.

Throughout the book, we will emphasize the importance of understanding the underlying mathematics and statistical principles that govern stochastic processes. We will provide detailed explanations of the theoretical concepts and illustrate them with examples and exercises to help students grasp the material.

In conclusion, this book serves as an introductory guide to the theory of stochastic processes, particularly suited for undergraduate or beginning graduate students. It provides a comprehensive coverage of key concepts, models, and applications, and emphasizes the importance of understanding the underlying mathematics and statistical principles. By the end of this book, students will have a solid foundation in stochastic processes and will be able to apply them to real-world problems.

Weight: 872g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030459840
Edition number: 2nd ed. 2020