Probability: An Introduction Through Theory and Exercises (Paperback)
Baldi, Paolo
- 出版商: Springer
- 出版日期: 2024-01-10
- 售價: $2,830
- 貴賓價: 9.5 折 $2,689
- 語言: 英文
- 頁數: 389
- 裝訂: Quality Paper - also called trade paper
- ISBN: 3031384911
- ISBN-13: 9783031384912
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商品描述
This textbook offers a complete one-semester course in probability, covering the essential topics necessary for further study in the areas of probability and statistics.
The book begins with a review of the fundamentals of measure theory and integration. Probability measures, random variables, and their laws are introduced next, along with the main analytic tools for their investigation, accompanied by some applications to statistics. Questions of convergence lead to classical results such as the law of large numbers and the central limit theorem with their applications also to statistical analysis and more. Conditioning is the next main topic, followed by a thorough introduction to discrete time martingales. Some attention is given to computer simulation. Through the text, over 150 exercises with full solutions not only reinforce the concepts presented, but also provide students with opportunities to develop their problem-solving skills, and make this textbook suitable forguided self-study.
Based on years of teaching experience, the author's expertise will be evident in the clear presentation of material and the carefully chosen exercises. Assuming familiarity with measure and integration theory as well as elementary notions of probability, the book is specifically designed for teaching in parallel with a first course in measure theory. An invaluable resource for both instructors and students alike, it offers ideal preparation for further courses in statistics or probability, such as stochastic calculus, as covered in the author's book on the topic.
商品描述(中文翻譯)
這本教科書提供了一個完整的一學期概率課程,涵蓋了進一步研究概率和統計領域所需的基本主題。
該書首先回顧了測度理論和積分的基礎知識。接下來介紹了概率測度、隨機變量及其定律,以及用於研究它們的主要分析工具,並附帶一些統計學應用。收斂問題引出了像大數定律和中心極限定理這樣的經典結果,並將它們應用於統計分析等方面。接下來是條件概率的主要主題,然後是對離散時間鞅的詳細介紹。一些注意力也被給予了計算機模擬。通過全文,超過150個帶有完整解答的練習不僅強化了所介紹的概念,還為學生提供了發展解決問題能力的機會,使這本教科書適合自學。
基於多年的教學經驗,作者的專業知識在材料的清晰呈現和精心選擇的練習中得以體現。假設讀者熟悉測度和積分理論以及概率的基本概念,該書特別設計用於與測度理論的第一門課程同步教學。這是教師和學生的寶貴資源,為進一步的統計學或概率學課程(如作者關於該主題的書中所涵蓋的隨機微積分)提供了理想的準備。
作者簡介
Paolo Baldi is professor at the University of Rome "Tor Vergata". He previously held positions at the universities of Catania and Pisa in Italy and also many visiting positions at the universities of Nanterre and Pierre et Marie Curie (now Sorbonne Université) in France. The author of more than 50 journal articles and 6 books (mainly textbooks), his research has focused on stochastic processes, in particular stochastic modeling on algebraic and geometric structures, as well as large deviations and numerical applications.
作者簡介(中文翻譯)
Paolo Baldi是羅馬“托爾韋爾加塔”大學的教授。他曾在意大利的卡塔尼亞大學和比薩大學擔任職位,並在法國的南特大學和皮埃爾·瑪麗·居里大學(現為巴黎索邦大學)擔任過多個訪問職位。作為50多篇期刊文章和6本書(主要是教科書)的作者,他的研究主要集中在隨機過程上,特別是代數和幾何結構上的隨機建模,以及大偏差和數值應用。