Probability and Stochastic Processes (Hardcover)

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.

《概率和隨機過程》是一本全面且易於理解的書籍，強調關鍵的理論概念和實際應用。該書以精緻的方式平衡理論和應用，以教學和易於理解的格式呈現。該書的主要重點是概率的關鍵理論概念，為理解與隨機過程相關的概念和例子提供基礎。

該書分為兩個主要部分，首先發展概率理論，涵蓋概率測度、隨機變量、積分理論、乘積空間、條件分佈和條件期望以及極限定理等主題。第二部分探討隨機過程及相關概念，包括泊松過程、更新過程、馬可夫鏈、半馬可夫過程、鞅和布朗運動。《概率和隨機過程》結合了傳統和複雜理論以及實踐，還包括：

- 來自商業、數學金融和工程等學科的多個例子
- 每章的練習和例子，讓讀者測試對所學材料的理解
- 對所有概率和隨機過程概念的嚴格處理

《概率和隨機過程》是高年級本科和研究生數學、商業和電氣工程概率和隨機過程課程的適當教材，也是數學、工程和金融領域的研究人員和從業人員的理想參考書。