第10版《随机过程概率模型入门》英文版概览

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《应用随机过程概率模型导论》(第10版)英文是一本经典的学术著作，由Sheldon M. Ross撰写，他本人是南加州大学的教授。该书旨在介绍和深入探讨概率模型在实际应用中的理论与实践。作为第十版，它反映了作者对随机过程领域的最新理解和研究成果，这门学科是统计学、信号处理、通信工程、金融数学以及许多其他科学和工程领域中的核心工具。本书覆盖了概率论的基础概念，包括随机变量、随机过程、马尔可夫链、布朗运动、泊松过程等，这些都是构建随机系统和分析随机现象的重要基石。读者可以从中学习到如何运用这些模型来描述和预测不确定性，尤其是在动态环境下的行为和变化。每一章都通过实例和习题进行深入解析，帮助读者逐渐掌握复杂的理论概念，并将其应用于解决实际问题。该书的特点在于其实用性和理论结合紧密，不仅适合正在攻读相关专业的研究生和高级本科生，也对研究者、工程师以及对随机过程感兴趣的业界人士具有参考价值。版权方面，所有内容受Elsevier公司保护，未经许可，不得以任何形式复制或传播，具体版权政策可在出版社网站上查询。通过阅读这本书，读者将能够提升对随机过程的理解，培养在实际工作中应用概率模型的能力，这对于在信息技术、通信技术、金融风险管理和自然科学等多个领域的专业人士来说，是一项不可或缺的技能提升。《应用随机过程概率模型导论》（第10版）是一部既严谨又实用的教科书，对于想要深入了解随机过程及其在现代科技中的应用的人来说，是一份宝贵的参考资料。

Preface xv

Jean Lemaire, University of Pennsylvania

Andrew Lim, University of California, Berkeley

George Michailidis, University of Michigan

Donald Minassian, Butler University

Joseph Mitchell, State University of New York, Stony Brook

Krzysztof Osfaszewski, University of Illinois

Erol Pekoz, Boston University

Evgeny Poletsky, Syracuse University

James Propp, University of Massachusetts, Lowell

Anthony Quas, University of Victoria

Charles H. Roumeliotis, Proofreader

David Scollnik, University of Calgary

Mary Shepherd, Northwest Missouri State University

Galen Shorack, University of Washington, Seattle

Marcus Sommereder, Vienna University of Technology

Osnat Stramer, University of Iowa

Gabor Szekeley, Bowling Green State University

Marlin Thomas, Purdue University

Henk Tijms, Vrije University

Zhenyuan Wang, University of Binghamton

Ward Whitt, Columbia University

Bo Xhang, Georgia University of Technology

Julie Zhou, University of Victoria

2 Introduction to Probability Theory

Some examples are the following.

1. If the experiment consists of the ﬂipping of a coin, then

S ={H, T}

where H means that the outcome of the toss is a head and T that it is a tail.

2. If the experiment consists of rolling a die, then the sample space is

S ={1, 2, 3, 4, 5, 6}

where the outcome i means that i appeared on the die, i = 1, 2, 3, 4, 5, 6.

3. If the experiments consists of ﬂipping two coins, then the sample space consists of the

following four points:

S ={(H, H), (H, T), (T, H), (T, T)}

The outcome will be (H, H) if both coins come up heads; it will be (H, T) if the

ﬁrst coin comes up heads and the second comes up tails; it will be (T, H) if the

ﬁrst comes up tails and the second heads; and it will be (T, T) if both coins come

up tails.

4. If the experiment consists of rolling two dice, then the sample space consists of the

following 36 points:

S =

⎧

⎪

⎨

⎪

⎩

(1, 1), (1, 2), (1, 3), (1,

4), (1,

5), (1, 6)

(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)

(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)

(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)

(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5,

(6,

1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)

⎫

⎪

⎬

⎪

⎭

where the outcome (i, j ) is said to occur if i appears on the ﬁrst die and j on the second

die.

5. If the experiment consists of measuring the lifetime of a car, then the sample space

consists of all nonnegative real numbers. That is,

S =[0, ∞)

∗



Any subset E of the sample space S is known as an event. Some examples of

events are the following.



. In Example (1), if E ={H}, then E is the event that a head appears on the ﬂip of the

coin. Similarly, if E ={T}, then E would be the event that a tail appears.



. In Example (2), if E ={1}, then E is the event that one appears on the roll of the

die. If E ={2, 4, 6}, then E would be the event that an even number appears on

the roll.

∗

The set (a, b) is deﬁned to consist of all points x such that a < x < b. The set [a, b] is deﬁned

to consist of all points x such that a  x  b. The sets (a, b] and [a, b) are deﬁned, respectively, to

consist of all points x such that a < x  b and all points x such that a  x < b.

1.2 Sample Space and Events 3



. In Example (3), if E ={(H, H), (H, T)}, then E is the event that a head appears on

the ﬁrst coin.



. In Example (4), if E ={(1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1)}, then E is the event

that the sum of the dice equals seven.



. In Example (5), if E = (2, 6), then E is the event that the car lasts between two and six

years. 

We say that the event E occurs when the outcome of the experiment lies in E.

For any two events E and F of a sample space S we deﬁne the new event E ∪ F

to consist of all outcomes that are either in E or in F or in both E and F. That is,

the event E ∪ F will occur if either E or F occurs. For example, in (1) if E ={H}

and F ={T}, then

E ∪ F ={H, T}

That is, E ∪ F would be the whole sample space S. In (2) if E ={1, 3, 5} and

F ={1, 2, 3}, then

E ∪ F ={1, 2, 3, 5}

and thus E ∪ F would occur if the outcome of the die is 1 or 2 or 3 or 5. The

event E ∪ F is often referred to as the union of the event E and the event F.

For any two events E and F, we may also deﬁne the new event EF, sometimes

written E ∩F, and referred to as the intersection of E and F,

follows. EF consists

of all outcomes which are both in E and in F. That is, the event EF will occur

only if both E and F occur. For example, in (2) if E ={1, 3, 5} and F ={1, 2, 3},

then

EF ={1, 3}

and thus EF would occur if the outcome of the die is either 1 or 3. In Exam-

ple (1) if E ={H} and F ={T}, then the event EF would not consist of any

outcomes and hence could not occur. To give such an event a name, we shall

refer to it as the null event and denote it by Ø. (That is, Ø refers to the event

consisting of no outcomes.) If EF = Ø, then E and F are said to be mutually

exclusive.

We also deﬁne unions and intersections of more than two events in a simi-

lar manner. If E

, E

, ... are events, then the union of these events, denoted by



∞

n=1

, is deﬁned to be the event that consists of all outcomes that are in E

for at least one value of n = 1, 2, .... Similarly, the intersection of the events E

denoted by



∞

n=1

, is deﬁned to be the event consisting of those outcomes that

are in all of the events E

, n = 1, 2, ... .

Finally, for any event E we deﬁne the new event E

, referred to as the

complement of E, to consist of all outcomes in the sample space S that are not

in E. That is, E

will occur if and only if E does not occur. In Example (4)

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