Most introductory textbooks on stochastic processes which cover standard topics such as Poisson process, Brownian motion, renewal theory and random walks deal inadequately with their applications. Written in a simple and accessible manner, this book addresses that inadequacy and provides guidelines and tools to study the applications. The coverage includes research developments in Markov property, martingales, regenerative phenomena and Tauberian theorems, and covers measure theory at an elementary level.

Contents:

• A Review of Probability Distributions and Their Properties
• Definition and Characteristics of a Stochastic Process
• Some Important Classes of Stochastic Processes
• Stationary Processes
• The Brownian Motion and the Poisson Process: Lévy Processes
• Renewal Processes and Random Walks
• Martingales in Discrete Time
• Branching Processes
• Regenerative Phenomena
• Markov Chains
• Tauberian Theorems
• Some Asymptotic Relations