Probability and Stochastic Processes
Emphasizing key theoretical concepts while incorporating real-world applications, Probability and Stochastic Processes presents a rigorous approach to probability and uses it as a foundation for understanding concepts and examples related to stochastic processes. Extensively classroom-tested, the material is both motivating and comprehensive. Engaging real-world applications and novel examples from business, mathematical finance, and engineering shed light on the topic's relevance in modern research. Topics of coverage are mathematically rigorous but also incorporate traditional applied concepts so that upper-undergraduate and graduate students can gain an intuitive sense of theory and its practice.
A comprehensive and accessible presentation of probability and stochastic processes with emphasis on key theoretical concepts and real-world applications
With a sophisticated approach, Probability and Stochastic Processes successfully balances theory and applications in a pedagogical and accessible format. The book's primary focus is on key theoretical notions in probability to provide a foundation for understanding concepts and examples related to stochastic processes.
Organized into two main sections, the book begins by developing probability theory with topical coverage on probability measure; random variables; integration theory; product spaces, conditional distribution, and conditional expectations; and limit theorems. The second part explores stochastic processes and related concepts including the Poisson process, renewal processes, Markov chains, semi-Markov processes, martingales, and Brownian motion. Featuring a logical combination of traditional and complex theories as well as practices, Probability and Stochastic Processes also includes:
Multiple examples from disciplines such as business, mathematical finance, and engineering
Chapter-by-chapter exercises and examples to allow readers to test their comprehension of the presented material
A rigorous treatment of all probability and stochastic processes concepts
An appropriate textbook for probability and stochastic processes courses at the upper-undergraduate and graduate level in mathematics, business, and electrical engineering, Probability and Stochastic Processes is also an ideal reference for researchers and practitioners in the fields of mathematics, engineering, and finance.
With a sophisticated approach, Probability and Stochastic Processes successfully balances theory and applications in a pedagogical and accessible format. The book's primary focus is on key theoretical notions in probability to provide a foundation for understanding concepts and examples related to stochastic processes.
Organized into two main sections, the book begins by developing probability theory with topical coverage on probability measure; random variables; integration theory; product spaces, conditional distribution, and conditional expectations; and limit theorems. The second part explores stochastic processes and related concepts including the Poisson process, renewal processes, Markov chains, semi-Markov processes, martingales, and Brownian motion. Featuring a logical combination of traditional and complex theories as well as practices, Probability and Stochastic Processes also includes:
Multiple examples from disciplines such as business, mathematical finance, and engineering
Chapter-by-chapter exercises and examples to allow readers to test their comprehension of the presented material
A rigorous treatment of all probability and stochastic processes concepts
An appropriate textbook for probability and stochastic processes courses at the upper-undergraduate and graduate level in mathematics, business, and electrical engineering, Probability and Stochastic Processes is also an ideal reference for researchers and practitioners in the fields of mathematics, engineering, and finance.
