Markov Processes and Potential Theory
Markov Processes and Potential Theory
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DOI：
10.1080/00401706.1969.10490719
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发表时间：
2007-12
期刊：
影响因子：
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通讯作者：
J. Doob;J. Chover
中科院分区：
文献类型：
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作者：
J. Doob;J. Chover
另一个例子是在第26页，定义3.1，其中定义了7次投掷硬币中H的个数的期望值。如果没有解释如何获得方程，虽然提到期望值是整数I到n的加权平均值，但学生面临的是试图理解期望的概念。直到第88页，定义7.4，才定义了随机变量的期望值。这本书有许多突出的特点。一是表述风格简洁明了。每一章都有许多例子。大多数定义后面都有例子，便于阅读。练习遵循章节中的大部分。证明是众多的整个文本，并在一般情况下，明确和非常完整。一个学期的课程可以很容易地涵盖本书的所有内容。总之，这本书既可以作为文本，也可以作为自学的工具。根据作者的既定目标，这门课将是最吸引那些对公理数学感兴趣的读者。那些读者更感兴趣的概率应用可能会发现其他文本更适合他们的需要。John A.康奈尔
Another example is on page 26, Definition 3.1, where the expected value of the Number of H’s in 7~ tosses of a coin is defined. Without an explanation as to how the equation was obtained, although it is mentioned that the expected value is a weighted average of the integers I through n, the student is confronted with trying to understand the concept of expectation. Not until page 88, Definition 7.4, is the expected value of a random variable defined. There are a number of outstanding features of this book. First, the style of presentation is concise and clear. Each chapter contains numerous examples. Most of the definitions are followed by examples, facilitating the reading. Exercises follow most sections within the chapters. Proofs are numerous throughout the text and are, in general, clear and very complete. A one-semester course could easily cover all the material in this book. To summarize, this book can be used either as a text or as a vehicle for self study. In accordance with the author’s stated objective, this course will be most, appealing to those readers interested in axiomatic mathematics. Those readers more interested in the applications of probability may find other texts more suitable to their needs. John A. Cornell