An Introduction to Applied Probability
Brémaud, Pierre
- 出版商: Springer
- 出版日期: 2024-05-04
- 售價: $3,070
- 貴賓價: 9.5 折 $2,917
- 語言: 英文
- 頁數: 492
- 裝訂: Hardcover - also called cloth, retail trade, or trade
- ISBN: 3031493052
- ISBN-13: 9783031493058
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商品描述
This book provides the elements of probability and stochastic processes of direct interest to the applied sciences where probabilistic models play an important role, most notably in the information and communications sciences, computer sciences, operations research, and electrical engineering, but also in fields like epidemiology, biology, ecology, physics, and the earth sciences.
The theoretical tools are presented gradually, not deterring the readers with a wall of technicalities before they have the opportunity to understand their relevance in simple situations. In particular, the use of the so-called modern integration theory (the Lebesgue integral) is postponed until the fifth chapter, where it is reviewed in sufficient detail for a rigorous treatment of the topics of interest in the various domains of application listed above.
The treatment, while mathematical, maintains a balance between depth and accessibility that is suitable for theefficient manipulation, based on solid theoretical foundations, of the four most important and ubiquitous categories of probabilistic models:
The theoretical tools are presented gradually, not deterring the readers with a wall of technicalities before they have the opportunity to understand their relevance in simple situations. In particular, the use of the so-called modern integration theory (the Lebesgue integral) is postponed until the fifth chapter, where it is reviewed in sufficient detail for a rigorous treatment of the topics of interest in the various domains of application listed above.
The treatment, while mathematical, maintains a balance between depth and accessibility that is suitable for theefficient manipulation, based on solid theoretical foundations, of the four most important and ubiquitous categories of probabilistic models:
- Markov chains, which are omnipresent and versatile models in applied probability
- Poisson processes (on the line and in space), occurring in a range of applications from ecology to queuing and mobile communications networks
- Brownian motion, which models fluctuations in the stock market and the "white noise" of physics
- Wide-sense stationary processes, of special importance in signal analysis and design, as well as in the earth sciences.
商品描述(中文翻譯)
本書提供了概率和隨機過程的要素,這些要素對應用科學領域非常重要,特別是在信息和通信科學、計算機科學、運籌學和電氣工程等領域,但也包括流行病學、生物學、生態學、物理學和地球科學等領域。理論工具逐步呈現,不會在讀者還沒有機會理解其在簡單情境中的相關性之前,用大量的技術性內容嚇退讀者。特別是,所謂的現代積分理論(勒貝格積分)的使用被推遲到第五章,在該章中對其進行了足夠詳細的回顧,以便嚴謹地處理上述各個應用領域中感興趣的主題。本書的處理方式雖然是數學的,但在深度和易讀性之間保持了平衡,適合於基於堅實的理論基礎對四個最重要且無所不在的概率模型進行高效操作,這四個模型是:馬爾可夫鏈(在應用概率中無所不在且多功能的模型)、泊松過程(在生態學到排隊和移動通信網絡等各種應用中出現)、布朗運動(模擬股市波動和物理學中的“白噪聲”)以及寬平穩過程(在信號分析和設計以及地球科學中非常重要)。本書可以以不同的方式和不同的學習水平使用。基本上,它為應用數學系的概率和隨機過程的兩學期研究生課程提供了教材,也適用於隨機模型在其他學科中起到關鍵作用的學生。概念和工具的逐步引入,以及包含大量示例,也使本書非常適合自學。
作者簡介
Pierre Brémaud graduated from the École Polytechnique and obtained his Doctorate in Mathematics from the University of Paris VI and his PhD from the department of Electrical Engineering and Computer Science at the University of California, Berkeley. He is a major contributor to the theory of stochastic processes and their applications, and has authored or co-authored several reference books and textbooks.
作者簡介(中文翻譯)
Pierre Brémaud畢業於École Polytechnique,並在巴黎第六大學獲得數學博士學位,同時也在加州大學伯克利分校的電機工程與計算機科學系獲得博士學位。他是隨機過程及其應用理論的重要貢獻者,並撰寫或合著了多本參考書籍和教科書。